Showing papers in "Ricerche Di Matematica in 2022"

$$n^2$$ of dissipative couplings are sufficient to guarantee the exponential decay in elasticity

Abstract: Abstract In this paper, we prove that the solutions to the problem determined by an elastic material with $$n^2$$ n 2 coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than $$n^2$$ n 2 (2 in dimension 2 and 6 in dimension 3).

A kinetic model of polyatomic gas with resonant collisions

Abstract: We propose a kinetic model describing a polyatomic gas undergoing resonant collisions, in which the microscopic internal and kinetic energies are separately conserved during a collision process. This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO $$_2$$ molecules. We discuss the model itself, prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We eventually present a numerical illustration of the model and its main properties.

Spatial regularity for a class of degenerate Kolmogorov equations

Abstract: We establish spatial a priori estimates for the solution u to a class of dilation invariant Kolmogorov equation, where u is assumed to only have a certain amount of regularity in the diffusion’s directions, i.e. $$x_{1}, \ldots , x_{m_{0}}$$ . The result is that u is also regular with respect to the remaining directions. The approach we propose is based on the commutators identities and allows us to obtain a Sobolev exponent that does not depend on the integrability assumption of the right-hand side. Lastly, we provide a new proof for the optimal spatial regularity.

Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications

Abstract: This study introduces a new lifetime distribution called the transmuted lower record type inverse Rayleigh which extends the inverse Rayleigh distribution and has the potential to model the recovery times of Covid-19 patients.The new distribution is obtained using the distributions of the first two lower record statistics of the inverse Rayleigh distribution. We discuss some statistical inferences and mathematical properties of the suggested distribution. We examine some characteristics of the proposed distribution such as density shape, hazard function,moments, moment generating function, incomplete moments,Rényi entropy, order statistics, stochastic ordering. We consider five estimation methods such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, Cramér-von Mises for the point estimation of the proposed distribution. Then, a comprehensive Monte Carlo simulation study is carried out to assess the risk behavior of the examined estimators. We provide two real data applications to illustrate the fitting ability of the proposed model, and compare its fit with competitor ones. Unlike many previously proposed distributions, the introduced distribution in this paper has modeled the recovery times of Covid-19 patients.

Periodic unfolding for lattice structures

Abstract: Abstract This paper deals with the periodic unfolding for sequences defined on one dimensional lattices in $${\mathbb {R}}^N$$ R N . In order to transfer the known results of the periodic unfolding in $${\mathbb {R}}^N$$ R N to lattices, the investigation of functions defined as interpolation on lattice nodes play the main role. The asymptotic behavior for sequences defined on periodic lattices with information until the first and until the second order derivatives are shown. In the end, a direct application of the results is given by homogenizing a 4th order Dirichlet problem defined on a periodic lattice.

How the nature of behavior change affects the impact of asymptomatic coronavirus transmission

Abstract: SARS-CoV-2 has caused severe respiratory illnesses and deaths since late 2019 and spreads globally. While asymptomatic cases play a crucial role in transmitting COVID-19, they do not contribute to the observed prevalence, which drives behavior change during the pandemic. This study aims to identify the effect of the proportion of asymptomatic infections on the magnitude of an epidemic under behavior change scenarios by developing a compartmental mathematical model. In this interest, we discuss three different behavior change cases separately: constant behavior change, instantaneous behavior change response to the disease’s perceived prevalence, and piecewise constant behavior change response to government policies. Our results imply that the proportion of asymptomatic infections which maximizes the spread of the epidemic depends on the nature of the dominant force driving behavior changes.

Stability of plane shear flows in a layer with rigid and stress-free boundary conditions

Abstract: Abstract We study the stability of shear flows of an incompressible fluid contained in a horizontal layer. We consider rigid–rigid, rigid—stress-free and stress-free—stress-free boundary conditions. We study (and recall some known results) linear stability/instability of the basic Couette, Poiseuille and a laminar parabolic flow with the spectral analysis by using the Chebyshev collocation method. We then use an $$L_2$$ L 2 -energy with Lyapunov second method to obtain nonlinear critical Reynolds numbers, by solving a maximum problem arising from the Reynolds energy equation. We obtain this maximum (which gives the minimum Reynolds number) for streamwise perturbations $$\mathrm{Re}_c={\text {Re}}^y$$ Re c = Re y . However, this contradicts a theorem which proves that streamwise perturbations are always stabilizing, $${\text {Re}}^y=+\infty $$ Re y = + ∞ . We solve this contradiction with a conjecture and prove that the critical nonlinear Reynolds numbers are obtained for two-dimensional perturbations, the spanwise perturbations, $$\mathrm{Re}_c={\text {Re}}^x$$ Re c = Re x , as Orr had supposed in the classic case of Couette flow between rigid planes.

Existence result and approximation of an optimal control problem for the Perona–Malik equation

Abstract: Abstract We discuss some optimal control problem for the evolutionary Perona–Malik equations with the Neumann boundary condition. The control variable v is taken as a distributed control. The optimal control problem is to minimize the discrepancy between a given distribution $$u_d\in L^2(\Omega )$$ u d ∈ L 2 ( Ω ) and the current system state. Since we cannot expect to have a solution of the original boundary value problem for each admissible control, we make use of a variant of its approximation using the model with fictitious control in coefficients of the principle elliptic operator. We introduce a special family of regularized optimization problems for linear parabolic equations and show that each of these problems is consistent, well-posed, and their solutions allow to attain (in the limit) an optimal solution of the original problem as the parameter of regularization tends to zero.

A nonlinear SAIR epidemic model: Effect of awareness class, nonlinear incidences, saturated treatment and time delay

Abstract: Awareness plays a vital role in informing and educating people about infection risk during an outbreak and hence helps to reduce the epidemic’s health burden by lowering the peak incidence. Therefore, this paper studies a susceptible-aware-infected-recovered (SAIR) epidemic model with the novel combinations of Michaelis-Menten functional type nonlinear incidence rates for unaware and aware susceptible with the inclusion of time delay as a latent period and a saturated treatment rate for infected people. The model is analyzed mathematically to describe disease transmission dynamics in two obtained equilibria: disease-free and endemic. We derive the basic reproduction number $$R_0$$ and investigate the local and global stability behavior of obtained equilibria for the time delay . A bifurcation analysis is performed using center manifold theory when there is no time delay, revealing the forward bifurcation when $$R_0$$ varies from unity. Moreover, the presence of Hopf bifurcation around EE is shown depending on the bifurcation parameter time delay. Lastly, the numerical simulations validate the analytical findings.

Anisotropic (p, q)-equations with superlinear reaction

Abstract: In this paper, we consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian and a superlinear reaction which need not satisfy the Ambrosetti–Robinowitz condition. By using variational tools together with truncation and comparison techniques and critical groups, we show the existence of at least five nontrivial smooth solutions, all with sign information: two positive, two negative and a nodal (sign-changing).

Almost symmetric good semigroups

Abstract: Abstract The class of good semigroups is a class of subsemigroups of $${\mathbb {N}}^h$$ N h , that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this paper we give a characterization of almost symmetric good subsemigroups of $${\mathbb {N}}^h$$ N h , extending known results in numerical semigroup theory and in one-dimensional ring theory, and we apply these results to obtain new results on almost Gorenstein one-dimensional analytically unramified rings.

Central random choice methods for hyperbolic conservation laws

Abstract: Abstract In this article, we briefly review the random choice method (RCM) and ADER methods for solving one and two-dimensional hyperbolic conservation laws. The main advantage of RCM is that it computes discontinuities with infinite resolution. In this method, the original problem is reduced to a set of local Riemann problems (RPs). The exact solutions of these RPs are used to form the solution of the original problem. However, RCM has the following disadvantages: (1) one should solve the RP exactly, however, the exact solutions are usually complex and unavailable for many problems. (2) The accuracy of the smooth region of the flow is poor. ADER methods are explicit, one-step schemes with a very high order of accuracy in time and space. They depend on the solution of the generalized RP (GRP) exactly. In Zahran (J Math Anal Appl 346:120–140, 2008), an improved version of ADER methods (central ADER) was introduced where the RPs were solved numerically and used central fluxes, instead of upwind fluxes. The improved central ADER schemes are more accurate, faster, simple to implement, RP solver free, and need less computer memory. To fade the drawbacks of the above schemes and keep their advantages, we propose, in this paper, an improved version of the RCM. We merge the central ADER technique with the RCM. The resulting scheme is called Central RCM (CRCM). The improvements are listed as follows: we use the WENO reconstruction for the initial data instead of constant reconstruction in RCM, we solve the RPs numerically by using central finite difference schemes and use random sampling to update the solution, as the original RCM. Here we use the staggered and non-staggered RCM. To enhance the accuracy of the new methods, we use a third-order TVD flux (Zahran in Bull Belg Math Soc Simon Stevin 14:259–275, 2007), instead of a first-order flux. Compared with the original RCM and the central ADER, the new methods combine the advantages of RCM, ADER, and central finite difference methods as follows: more accurate, very simple to implement, need less computer memory, and RP solver free. Moreover, the new methods capture the discontinuities with infinite resolution and improve the accuracy of the smooth parts. The new methods have less CPU time than the central ADER methods, this is due to less flux evaluation in CRCM. An extension of the schemes to general systems of nonlinear hyperbolic conservation laws in one and two dimensions is presented. We present several numerical examples for one and two-dimensional problems. The results confirm that the presented schemes are superior to the original RCM, ADER, and central ADER schemes.