Showing papers in "Ricerche Di Matematica in 2019"
TL;DR: In this article, the existence and stability of stationary square and super-square patterns was studied by performing a close to equilibrium asymptotic weakly nonlinear expansion, and the emergence of these patterns was shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance.
Abstract: We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
30 citations
TL;DR: In this paper, a predator-prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction diffusion system, following the approach proposed in the context of ODEs by Geritz and Gyllenberg.
Abstract: A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the approach proposed in the context of ODEs by Geritz and Gyllenberg (J Theor Biol 314:106–108, 2012). Part of this derivation can be made rigorous. The possibility of appearance of Turing patterns for this cross-diffusion system is studied, and compared to what happens when standard diffusion terms replace the cross-diffusion terms.
17 citations
TL;DR: In this paper, a first order quasilinear hyperbolic system describing a polyatomic gas far from the equilibrium is considered, and classes of exact solutions parameterized in terms of arbitrary functions are determined.
Abstract: In this paper a first order quasilinear hyperbolic system describing a polyatomic gas far from the equilibrium is considered. After giving a classification of all the possible first order differential constraints admitted by the governing equations under interest, classes of exact solutions parameterized in terms of arbitrary functions are determined. That can help in solving initial or boundary value problems. Finally the consistency of the exact solutions characterized during the reduction procedure with the entropy principle is studied.
14 citations
TL;DR: In this article, the authors established the Hardy-Littlewood-Polya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces, and also gave the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators.
Abstract: This paper establishes the Hardy–Littlewood–Polya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces.
13 citations
TL;DR: In this article, the first-passage time problems for continuous-time birth-death chains are considered and recursive formulas for the moments of the first exit time and of first passage time in terms of the potential coefficients are explicitly obtained.
Abstract: First-passage time problems for continuous-time birth–death chains are considered. Recursive formulas for the moments of the first-exit time and of the first-passage time in terms of the potential coefficients are explicitly obtained. Making use of the probability current, some functional relations between transition probabilities for unrestricted and restricted continuous-time birth–death chains are determined. Finally, two continuous-time birth–death chains with constant rates are taken in account; for them, closed form results on the first-exit time and on the first-passage time are explicitly obtained.
13 citations
TL;DR: In this article, the onset of Hopf bifurcations in rotatory thermal hydrodynamics is studied and the Hopf Bifurcation number (threshold that the Taylor number crosses at the onset) is obtained.
Abstract: The onset of instability in autonomous dynamical systems (ADS) of ordinary differential equations is investigated. Binary, ternary and quaternary ADS are taken into account. The stability frontier of the spectrum is analyzed. Conditions necessary and sufficient for the occurring of Hopf, Hopf–Steady, Double-Hopf and unsteady aperiodic bifurcations—in closed form—and conditions guaranteeing the absence of unsteady bifurcations via symmetrizability, are obtained. The continuous triopoly Cournot game of mathematical economy is taken into account and it is shown that the ternary ADS governing the Nash equilibrium stability, is symmetrizable. The onset of Hopf bifurcations in rotatory thermal hydrodynamics is studied and the Hopf bifurcation number (threshold that the Taylor number crosses at the onset of Hopf bifurcations) is obtained.
13 citations
TL;DR: In this paper, the interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient was investigated, and it was shown that for slow time, waves are propagated almost undisturbed, while for fast time, diffusion effects prevail.
Abstract: A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient $$ \varepsilon $$
, is investigated. Results obtained prove that for slow time $$ \varepsilon t <1 $$
waves are propagated almost undisturbed, while for fast time $$ t>\frac{1}{\varepsilon } $$
diffusion effects prevail.
10 citations
TL;DR: In this article, the authors studied the nonequilibrium pressure and temperatures within the framework of extended thermodynamics of gases with 6 independent fields, and derived thermodynamic relations for these quantities from the entropy principle.
Abstract: We study the nonequilibrium pressure and temperatures within the framework of extended thermodynamics of gases with 6 independent fields. We derive thermodynamic relations for these quantities from the entropy principle. These relations indicate the usefulness of nonequilibrium thermodynamic potentials. We also introduce the nonequilibrium temperatures by using the caloric equation of state, and prove that the two different definitions of nonequilibrium temperature are equivalent to each other.
10 citations
TL;DR: In this article, the authors investigated the problem of sub-shocks in a binary mixture of monoatomic gases with a gradient 10-moment approximation of the Boltzmann equations.
Abstract: The problem of sub-shock occurrence within a shock structure solution is investigated for an inert binary mixture of monoatomic gases, modelled by a Grad 10-moment approximation of the Boltzmann equations. The main purpose of this paper is to show by numerical simulations the existence of discontinuous shock structure solutions for values of the shock speed below the maximum unperturbed characteristic velocity. Moreover, for suitable concentrations of the two species, and for shock velocities beyond the maximum unperturbed characteristic velocity, each constituent of the mixture generates a jump discontinuity, and the shock structure solution exhibits two sub-shocks.
9 citations
TL;DR: In this paper, the authors formulated a mathematical model to study the complex dynamical behavior of a three dimensional model consisting of one prey and two predators involving Beddington-DeAngelis and Crowley-Martin functional responses.
Abstract: We formulate a mathematical model to study the complex dynamical behavior of a three dimensional model consisting of one prey and two predators involving Beddington–DeAngelis and Crowley–Martin functional responses. The existence and stability conditions of the equilibrium points are analyzed. The global asymptotic stability of the interior equilibrium point, if exists, is proved by considering Lyapunov function. Several numerical simulations are performed to illustrate the theoretical analysis. The multiple states of stability are observed in one example whereas another example exhibits the global stability of interior equilibrium point.
9 citations
TL;DR: In this article, the authors studied radially symmetric solutions for the reaction-diffusion-chemotaxis model of multiple sclerosis and derived the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balo sclerosis and in the early phase of Multiple Sclerosis.
Abstract: In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balo sclerosis and in the early phase of Multiple Sclerosis. We present numerical simulations which illustrate and fit the analytical results.
TL;DR: In this article, the pole divisor of the wave function for real regular bounded multi-soliton KP-II solutions represented by points in the reducible rational plane-bipartite networks was constructed.
Abstract: We construct the pole divisor of the wavefunction for real regular bounded multi-soliton KP-II solutions represented by points in $$Gr^\mathrm{TP} (2,4)$$
on the reducible rational $$\mathtt M$$
-curve $$\varGamma ({\mathcal {N}}_T)$$
recently introduced in Abenda and Grinevich (KP theory, plane-bipartite networks in the disk and rational degenerations of $${\mathtt M}$$
-curves, 2018. arXiv:1801.00208
) and we give evidence that the asymptotic behavior of its zero divisor in the real (x, y)-plane at fixed time t is compatible with the behavior of the soliton solution classified in Chakravarty and Kodama (Stud Appl Math 123:83–151, 2009).
TL;DR: In this paper, the authors revisited the extended thermodynamic theory of dense polyatomic gases developed in the paper (Arima et al. in Phys Rev Fluids 2:013401, 2017) from the viewpoint of the energy exchange between two subsystems: the subsystem with the kinetic and potential energies and the subsystem of the internal modes such as molecular rotation and vibration.
Abstract: We revisit the extended thermodynamic (ET) theory of dense polyatomic gases developed in the paper (Arima et al. in Phys Rev Fluids 2:013401, 2017) from the viewpoint of the energy exchange between two subsystems: the subsystem with the kinetic and potential energies and the subsystem of the internal modes such as molecular rotation and vibration. We confirm that the system of balance equations derived from the viewpoint is completely the same as the previous one, but thereby we can obtain its complementary physical implications. We also point out a possible alternative procedure in the modeling method based on ET.
TL;DR: In this article, the onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed.
Abstract: The onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided.
TL;DR: Taniguchi and Ruggeri as discussed by the authors showed that for systems compatible with the entropy principle, continuous shock-structure solutions cannot exist when s is larger than the maximum characteristic velocity evaluated in the unperturbed state.
Abstract: For a generic hyperbolic system of balance laws, the shock-structure solution is not continuous and a discontinuous part (sub-shock) arises when the velocity of the front s is greater than a critical value. In particular, for systems compatible with the entropy principle, continuous shock-structure solutions cannot exist when s is larger than the maximum characteristic velocity evaluated in the unperturbed state $$s >\lambda ^{\max }_0 $$
. This is the typical situation of systems of Rational Extended Thermodynamics (ET). Nevertheless, in principle, sub-shocks may exist also for s smaller than $$\lambda ^{\max }_0 $$
. This was proved with a simple example in a recent paper by Taniguchi and Ruggeri (Int J Non-Linear Mech 99:69, 2018). In the present paper, we offer another simple case that satisfies all requirements of ET, that is, the entropy inequality, convexity of the entropy, sub-characteristic condition and Shizuta-Kawashima condition, however, there exists a sub-shock with s slower than $$\lambda ^{\max }_0 $$
. Therefore there still remains an open question which other property makes the systems coming from ET have this beautiful property that the sub-shock exists only for s greater than the unperturbed maximum characteristic velocity.
TL;DR: In this article, the onset of double-diffusive convection in horizontal porous layers for the Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated.
Abstract: The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.
TL;DR: In this article, an optimal control problem for the mixed Dirichlet-Neumann boundary value problem for strongly non-linear elliptic equation with p-Laplace operator and a density of surface traction u acting on a part of boundary of open domain is studied.
Abstract: In this paper we study an optimal control problem for the mixed Dirichlet–Neumann boundary value problem for the strongly non-linear elliptic equation with p-Laplace operator and $$L^1$$-nonlinearity in their right-hand side. A density of surface traction u acting on a part of boundary of open domain is taken as a boundary control. The optimal control problem is to minimize the discrepancy between a given distribution $$y_d\in L^2(\varOmega )$$ and the current system state. We deal with such case of nonlinearity when we cannot expect to have a solution of the state equation for any admissible control. After defining a suitable functional class in which we look for solutions and assuming that this problem admits at least one feasible solution, we prove the existence of optimal pairs. In order to handle the strong non-linearity in the right-hand side of elliptic equation, we involve a special two-parametric fictitious optimization problem. We derive existence of optimal solutions to the regularized optimization problems at each $$({\varepsilon },k)$$-level of approximation and discuss the asymptotic behaviour of the optimal solutions to regularized problems as the parameters $${\varepsilon }$$ and k tend to zero and infinity, respectively.
TL;DR: In this article, an existence result for a class of quasilinear parabolic problems with continuous coefficients blowing up for a finite value of the unknown, a second hand and an initial data was established.
Abstract: An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand $$\mu \in \mathcal {M}_{b}(Q)$$ and an initial data $$u_{0}\in L^{1}(\Omega )$$. We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some compactness results are also shown under additional hypotheses.
TL;DR: In this article, the authors studied non-reflexive Orlicz spaces and their Morse subspace and showed that the closure of a subspace in such spaces can be described as having an o-O type structure with respect to an equivalent norm on the subspace.
Abstract: We study non reflexive Orlicz spaces $$L^\varPsi $$ and their Morse subspace $$M^\varPsi $$, i.e. the closure of $$L^\infty $$ in $$M^\varPsi $$ to determine when $$(M^\varPsi ,L^\varPsi )$$ can be described as having an o–O type structure with respect to an equivalent norm on $$L^\varPsi $$. Examples of classes of Young functions for which the answer is affirmative are provided, but also examples are given to show that this is not possible for all non-reflexive Orlicz spaces. An equivalent expression of the distance in $$L^\varPsi $$ to $$M^\varPsi $$, induced by the new norm, is also provided.
TL;DR: In this paper, a relativistic extended thermodynamics theory of polyatomic gas was proposed, which takes into account the energy exchange between the translational and the internal modes of a molecule in binary collisions.
Abstract: In a recent article (Ann Phys 377:414–445, 2017. https://doi.org/10.1016/j.aop.2016.12.012
), Pennisi and Ruggeri proposed a relativistic extended thermodynamics theory of polyatomic gas. It was achieved by adopting the closure procedure for the generalized moments of a distribution function that, as in the classical case, depends on an additional continuous variable representing the energy of the internal modes of a molecule; this permits the theory to take into account the energy exchange between the translational and the internal modes of a molecule in binary collisions. In this paper the attention will be focused on some integrals appearing in the field equations of the relativistic theory of polyatomic gas and their integrability will be proven. In the last part of the paper we consider the case of a monatomic gas and we evaluate the ultra-relativistic limit of the differential system of balance laws.
TL;DR: In this paper, a nonlinear model of extended thermodynamics with six fields without the near-equilibrium approximation, in one dimensional case, was considered and a class of double wave solutions of the governing system at hand was determined.
Abstract: A nonlinear model of extended thermodynamics with six fields without the near-equilibrium approximation, in one dimensional case, is considered. A class of double wave solutions of the governing system at hand is determined and an exact description of a soliton-like wave interaction is given.
TL;DR: In this article, a mixture of four gases undergoing a bimolecular irreversible reaction is investigated and the influence of Mach number, of concentrations in the unperturbed state and of the chemical energy is shown via numerical simulations.
Abstract: Steady deflagration waves are investigated for a mixture of four gases undergoing a bimolecular irreversible reaction. The influence of Mach number, of concentrations in the unperturbed state and of the chemical energy is shown via numerical simulations.
TL;DR: An innovation diffusion model with six-compartments for two different patches is proposed, where the entire population in both the patches is classified into three different groups: non-adopter, adopter of product-1, and adopters of products-2.
Abstract: The aim of the present paper, how the people behave towards the offer of two products in two different patches. In this work, an innovation diffusion model with six-compartments for two different patches is proposed. There is a delay in the adoption of product-1 in patch-2 and delay of adoption of product-2 in patch-1. The entire population in both the patches is classified into three different groups (i) non-adopter (ii) adopter of product-1 (iii) adopter of product-2. Dynamical behavior of the proposed system is studied, and Basic influence numbers (BINs) of the model are calculated. Stability analysis is executed for all the possible equilibrium points with and without delays. Hopf bifurcation analysis is too carried out taking the delay of adoption to adopt the product-1 in patch-2, and product-2 in patch-1 are bifurcation parameter and obtained the threshold values. Moreover, sensitivity analysis is carried out for the system parameter used in the interior equilibrium. Finally, exhaustive numerical simulations have been carried out by utilizing MATLAB, to supports analytical results.
TL;DR: In this paper, the authors prove that the functional decomposition of the 3D variational data assimilation (3D Var DA) operator is equivalent to applying multiplicative parallel Schwarz (MPS) method, to the Euler-Lagrange equations arising from the minimization of the DA functional.
Abstract: Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a big and computationally expensive problem. In the present work we prove that the functional decomposition of the 3D variational data assimilation (3D Var DA) operator, previously introduced by the authors, is equivalent to apply multiplicative parallel Schwarz (MPS) method, to the Euler–Lagrange equations arising from the minimization of the data assimilation functional. It results that convergence issues as well as mesh refininement techniques and coarse grid correction—issues of the functional decomposition not previously addressed—could be employed to improve performance and scalability of the 3D Var DA functional decomposition in real cases.
TL;DR: In this paper, it was shown that the lattice of all totally composition formations of finite groups is algebraic, and that all finite groups can be represented by a lattice.
Abstract: It is shown that the lattice of all totally composition formations of finite groups is algebraic.
TL;DR: In this paper, the authors studied the Dirichlet problem for two related equations involving the 1-Laplacian and a total variation term as reaction, and showed that a bounded solution exists if the datum f belongs to a regular, bounded domain in the Euclidean space.
Abstract: In this paper we study the Dirichlet problem for two related equations involving the 1-Laplacian and a total variation term as reaction, namely: with homogeneous Dirichlet boundary conditions on $$\partial \varOmega $$, where $$\varOmega $$ is a regular, bounded domain in $$\mathbb {R}^N$$. Here f is a measurable function belonging to some suitable Lebesgue space, while g(u) is a continuous function having the same sign as u and such that $$g(\pm \infty ) = \pm \infty $$. As far as Eq. (1) is concerned, we show that a bounded solution exists if the datum f belongs to $$L^N(\varOmega )$$. When the absorption term g(u) is missing, i.e. in the case of Eq. (2), we show that if $$f\in L^N(\varOmega )$$, and its norm is small, then the only solution of (2) is $$u\equiv 0$$. In the case where the norm of f is not small, several cases may happen. Depending on $$\varOmega $$ and f, we show examples where no solution of (2) exists, other examples where $$u\equiv 0$$ is still a solution, and finally examples with nontrivial solutions. Some of these results can be viewed as a translation to the 1-Laplacian operator of known results by Ferone and Murat.
TL;DR: In this paper, a general closed-form soliton solution formula for the classical Heisenberg ferromagnet equation with in-plane asymptotic conditions is obtained by means of the inverse scattering transform technique and the matrix triplet method.
Abstract: A new, general, closed-form soliton solution formula for the classical Heisenberg ferromagnet equation with in-plane asymptotic conditions is obtained by means of the inverse scattering transform technique and the matrix triplet method. This formula encompasses the soliton solutions already known in the literature as well as a new class of soliton solutions (the so-called multipole solutions), allowing their classification and description. Examples from all classes are provided and discussed.
TL;DR: In this paper, the authors studied the structure of a finite group under the assumption that every subgroup H of P with H = H|H|=|D|<|P|$$ is weakly s-semipermutable or ss-quasinormal in G.
Abstract: Suppose that G is a finite group and H is a subgroup of G. H is said to be weakly s-semipermutable in G if there are a subnormal subgroup T of G and an s-semipermutable subgroup $$H_{ssG}$$ of G contained in H such that $$G=HT$$ and $$H\cap T\le H_{ssG}$$; H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that $$G=HB$$ and H permutes with every Sylow subgroup of B. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying $$1<|D|<|P|$$ and study the structure of G under the assumption that every subgroup H of P with $$|H|=|D|$$ is either weakly s-semipermutable or ss-quasinormal in G. Some recent results are generalized and unified.
TL;DR: In this article, a density lower bound for functionals involving bulk and interfacial energies was proved for convex functions with p-power growth not subjected to any further structure conditions.
Abstract: We prove a density lower bound for some functionals involving bulk and interfacial energies. The bulk energies are convex functions with p-power growth not subjected to any further structure conditions. The interface $$\partial E$$ is the boundary of a set $$E\subset \Omega $$ such that $$|E|=d$$ is prescribed. Then we get $$\mathcal {H}^{n-1}((\partial E{\setminus }\partial E^*)\cup \Omega )=0$$.
TL;DR: It is shown that multiple endemic equilibria may coexist and that backward bifurcation takes place when the peer-pressure is strong enough and that the alcohol-free equilibrium is globally stable.
Abstract: In this paper, we propose and analyze a behavioral model for the spread of high-risk alcohol consumption The model is given by ordinary differential equations and includes a convex ‘force of persuasion’ that mimics the peer-pressure We also assume that the transmission rate depends on the current and the past history of alcohol abuse prevalence in the community and that the weight given to the past history is described by an n-order Erlangian kernel We perform a qualitative analysis based on stability and bifurcation theory We show that multiple endemic equilibria may coexist and that backward bifurcation takes place when the peer-pressure is strong enough We also use a Lyapunov stability approach to find sufficient conditions ensuring that the alcohol-free equilibrium is globally stable