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JournalISSN: 0035-5038

Ricerche Di Matematica 

Springer Science+Business Media
About: Ricerche Di Matematica is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Mathematics & Nonlinear system. It has an ISSN identifier of 0035-5038. Over the lifetime, 787 publications have been published receiving 4358 citations.


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TL;DR: In this paper, two mathematical models for phase segregation and diffusion of an order parameter are derived, within one and the same continuum mechanical framework, respectively of the Allen-Cahn type and of the Cahn-Hilliard type.
Abstract: Two mathematical models for phase segregation and diffusion of an order parameter are derived, within one and the same continuum mechanical framework. These models are, respectively, of the Allen-Cahn type and of the Cahn-Hilliard type. Our framework is similar to that used in [1], in that a postulated balance of microforces plays a central role in both deductive paths, but differs from it, mainly in three ways: imbalance of entropy replaces for a dissipation inequality, whose form depends on the case, restricting the growth of free energy; balance of energy replaces for the mass balance introduced in [1] to arrive at (a generalization of) the C-H equation; and chemical potential is given the same role played by coldness in the deduction of the heat equation. When appropriate constitutive prescriptions are made, different in the cases of segregation and diffusion but consistent with the entropy imbalance, it is found that standard A-C and C-H processes are solutions of constant chemical potential of the corresponding generalized equations; in particular, the stationary solutions are the same. Keywords: Phase segregation, Diffusion, Allen-Cahn equation, Cahn-Hilliard equation, Phase-field methods Mathematics Subject Classification (2000): 74N25, 74A50, 35K60

74 citations

Journal ArticleDOI
TL;DR: In this paper, the existence of positive ground states with minimal energy was shown in the case of an elliptic system and satisfying suitable assumptions, but not requiring any symmetry property on them.
Abstract: In this paper we consider the following elliptic system in $${\mathbb{R}^3}$$ $$\qquad\left\{\begin{array}{ll}-\Delta u+u+\lambda K(x)\phi u=a(x)|u|^{p-1}u \quad &x \in {\mathbb{R}}^{3}\\ -\Delta \phi=K(x)u^{2} \quad &x \in {\mathbb{R}}^{3}\end{array}\right.$$ where λ is a real parameter, $${p\in (1, 5)}$$ if λ < 0 while $${p\in (3, 5)}$$ if λ > 0 and K(x), a(x) are non-negative real functions defined on $${\mathbb{R}^3}$$ . Assuming that $${\lim_{|x|\rightarrow+\infty}K(x)=K_{\infty} >0 }$$ and $${\lim_{|x|\rightarrow+\infty}a(x)=a_{\infty} >0 }$$ and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive ground states, namely the existence of positive solutions with minimal energy.

72 citations

Journal ArticleDOI
TL;DR: In this article, an SEIR epidemic model with a nonlinear incidence rate is studied and the incidence is assumed to be a convex function with respect to the infective class of a host population.
Abstract: An SEIR epidemic model with a nonlinear incidence rate is studied The incidence is assumed to be a convex function with respect to the infective class of a host population A bifurcation analysis is performed and conditions ensuring that the system exhibits backward bifurcation are provided The global dynamics is also studied, through a geometric approach to stability Numerical simulations are presented to illustrate the results obtained analytically This research is discussed in the framework of the recent literature on the subject

62 citations

Journal ArticleDOI
TL;DR: In this article, a model based on a semilinear perturbation of the Maxwell equation (SME) is introduced, where the particles are described by the finite energy solitary waves of SME whose existence is due to the presence of the nonlinearity.
Abstract: In this paper we study a model which describes the relation of the matter and the electromagnetic field from a unitarian standpoint in the spirit of the ideas of Born and Infeld. This model, introduced in [1], is based on a semilinear perturbation of the Maxwell equation (SME). The particles are described by the finite energy solitary waves of SME whose existence is due to the presence of the nonlinearity. In the magnetostatic case (i.e. when the electric field ${\bf E}=0$ and the magnetic field ${\bf H}$ does not depend on time) the semilinear Maxwell equations reduce to semilinear equation where “ $ abla\times $ ” is the curl operator, f′ is the gradient of a smooth function $f:{\mathbb{R}}^3\to{\mathbb{R}}$ and ${\bf A}:{\mathbb{R}}^3\to{\mathbb{R}}^3$ is the gauge potential related to the magnetic field ${\bf H}$ ( ${\bf H}= abla\times {\bf A}$ ). The presence of the curl operator causes (1) to be a strongly degenerate elliptic equation. The existence of a nontrivial finite energy solution of (1) having a kind of cylindrical symmetry is proved. The proof is carried out by using a variational approach based on two main ingredients: the Principle of symmetric criticality of Palais, which allows to avoid the difficulties due to the curl operator, and the concentration-compactness argument combined with a suitable minimization argument. Keywords: Maxwell equations, Natural constraint, Minimizing sequence Mathematics Subject Classification (2000): 35B40, 35B45, 92C15

51 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide a review of some key literature results on the influence of seasonality and other time heterogeneities of contact rates, and other parameters, such as vaccination rates, on the spread of infectious diseases.
Abstract: We provide a review of some key literature results on the influence of seasonality and other time heterogeneities of contact rates, and other parameters, such as vaccination rates, on the spread of infectious diseases. This is a classical topic where highly theoretical methodologies have provided new insight on the seemingly random behavior observed in epidemic time-series. We follow the line of providing a highly personal non-systematic review of this topic, mainly based on the history of mathematical epidemiology and on the impact of reviewed articles. Our aim is to stress some issues of increasing interest, such as the public health implications of the biomathematical literature and the impact of seasonality on epidemic extinction or elimination.

47 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202341
202263
2021156
202066
201956
201861