Acta Applicandae Mathematicae最新文献

A vector-borne disease model with spatial diffusion with time delays and a general incidence function is studied. We derived conditions under which the system exhibits threshold behavior. The stability of the disease-free equilibrium and the endemic equilibrium are analyzed by using the linearization method and constructing appropriate Lyapunov functionals. It is shown that the given conditions are satisfied by at least two common forms of the incidence function.

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of ({mathcal{L}}_{p})-spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical (q)-Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution.

In this work we consider a semilinear plate equation with non-constant material density in the context of energy damping models. Existence and uniqueness of regular and generalized solutions are established. The energy associated to this equation is shown to posses a compressed polynomial decay range.

In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of (d) molecules where each molecule regulates its successor in a cycle ((A_{1}rightarrow A_{2}rightarrow cdots rightarrow A_{d-1} rightarrow A_{d} rightarrow A_{1})). Regulations, which can be either positive or negative, are modelled by increasing or decreasing functions. We make an analysis of this model for a wide range of functions (including affine and Hill functions) by determining the parameters for which bistability and oscillatory behaviours arise. These results encompass previous theoretical studies of gene regulatory networks, which are particular cases of this model.

In (mathbb{R}^{2}), a symmetric blunt body (W_{b}) is fixed by smoothing out the tip of a symmetric wedge (W_{0}) with the half-wedge angle (theta _{w}in (0, frac{pi }{2})). We first show that if a horizontal supersonic flow of uniform state moves toward (W_{0}) with a Mach number (M_{infty }>1) being sufficiently large depending on (theta _{w}), then the half-wedge angle (theta _{w}) is less than the detachment angle so that there exist two shock solutions, a weak shock solution and a strong shock solution, with the shocks being straight and attached to the vertex of the wedge (W_{0}). Such shock solutions are given by a shock polar analysis, and they satisfy entropy conditions. The main goal of this work is to construct a detached shock solution of the steady Euler system for inviscid compressible irrotational flow in (mathbb{R}^{2}setminus W_{b}). Especially, we seek a shock solution with the far-field state given as the strong shock solution obtained from the shock polar analysis. Furthermore, we prove that the detached shock forms a convex curve around the blunt body (W_{b}) if the Mach number of the incoming supersonic flow is sufficiently large, and if the boundary of (W_{b}) is convex.

This work is devoted to study the existence of least energy sign-changing solutions for a nonlocal weighted Schrödinger-Kirchhoff problem in the unit ball (B) of (mathbb{R}^{N}), (N>2). The non-linearity of the equation is assumed to have exponential growth in view of Trudinger-Moser type inequalities. In order to obtain our existence result, we use the constrained minimization in Nehari set, the quantitative deformation Lemma and degree theory results.

Introducing a logarithmic pressure, we analyze the phenomenon of concentration and the formation of delta-shocks for the generalized Chaplygin gas dynamics. We first solve the Riemann problem for the logarithmic perturbed model and construct the solutions with four kinds of structures (R_{1}+R_{2}), (R_{1}+S_{2}), (S_{1}+R_{2}) and (S_{1}+S_{2}). Then it is shown that when the logarithmic pressure vanishes, the limits of the Riemann solutions for the logarithmic perturbed model are just these of the generalized Chaplygin gas dynamics. In particular, when the initial data satisfy some certain conditions, the (S_{1}+S_{2}) solution of the logarithmic perturbed model tends to the delta-shock solution of the generalized Chaplygin gas dynamics. Finally, some numerical results exhibit the process of formation of delta-shocks.

Principal and nonprincipal solutions of differential equations play a critical role in studying the qualitative behavior of solutions in numerous related differential equations. The existence of such solutions and their applications are already documented in the literature for differential equations, difference equations, dynamic equations, and impulsive differential equations. In this paper, we make a contribution to this field by examining impulsive dynamic equations and proving the existence of such solutions for second-order impulsive dynamic equations. As an illustration, we prove the famous Leighton and Wong oscillation theorems for impulsive dynamic equations. Furthermore, we provide supporting examples to demonstrate the relevance and effectiveness of the results.

We provide a result on the existence of a positive periodic solution for the following class of delay equations

In particular, we find an infinite family of disjoint intervals having the following property: if the delay is within one of these intervals, then the equation admits a non-trivial and even (2r)-periodic solution. Furthermore, the length of these intervals is constant and depends on the size of the term (|f'(eta )|), where (eta ) is the unique positive equilibrium point of the equation. Consequently, we can find periodic solutions for arbitrarily large delays.

General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic (mathrm {L}_{p}) estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.