Acta Applicandae Mathematicae最新文献

Recently, several events have shockingly impacted society, carrying tough consequences. However, not all individuals are similarly affected by shock events. Among other factors, the consequences can vary depending on the income class. In our presented work, the approach typical of kinetic theory is used to analyze the dynamics of a closed-market society exposed to various types of shock events. To achieve this, we introduce non-conservative equations, incorporating proliferative and destructive binary interactions as well as external actions. Specifically, the latter term reproduces the shock events, and to accomplish this, we introduce an appropriate external force field into the kinetic framework, modeled using Gaussian functions. Several numerical simulations are presented to illustrate the behavior of the solution predicted by the model and an application in comparison to real data relative to the Hurricane Katrina catastrophe is carried out.

This paper proposes a reaction-diffusion epidemic model incorporating media coverage and vaccination strategies, and analyzes the transmission dynamics of diseases in spatially heterogeneous environments. The model innovatively considers the impact of environmental pollution on disease transmission and introduces nonlinear incidence rate functions to more accurately describe the disease transmission process. The study establishes the well-posedness of the model solution and calculates the basic reproduction number (mathcal{R}_{0}) using the next generation infection operator. We derive the corresponding threshold results and prove that the disease-free equilibrium is globally asymptotically stable when (mathcal{R}_{0}<1), while the disease persists when (mathcal{R}_{0}>1). In particular, for the spatially homogeneous case, we establish the existence and uniqueness of an endemic equilibrium when (mathcal{R}_{0}>1). Finally, numerical simulations validate the theoretical results and intuitively demonstrate the inhibitory effect of media coverage on disease transmission.

A numerical framework is developed for the analysis of a parameterized bidomain model in cardiac electrophysiology. Convergence to a weak solution is established through the derivation of appropriate a priori bounds, thereby proving the existence of a bounded weak solution to the problem. Numerical experiments validate the accuracy and robustness of the method, showcasing its effectiveness in accurately capturing the dynamics of electrical wave propagation in cardiac tissue.

To uncover the mechanism by which magnetic fields can stabilize electrically conducting turbulent fluids, we investigate the stability of a special three-dimensional anisotropic magnetohydrodynamic (MHD) system. This system features dissipation only in the direction of (x_{1}) and magnetic damping near a background magnetic field. Due to the absence of dissipation in the (x_{2}) and (x_{3}) directions, establishing the stability and long-time behavior of this MHD system is highly nontrivial. Through a subtle energy estimate and careful analysis of the nonlinearities, we rigorously justify the stability of this MHD system near a background magnetic field and derive explicit decay rates. The primary challenge lies in proving the uniform integrability of (|nabla _{h}u|_{L^{infty }}) in the time variable.

In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.

This paper investigates common variational inclusion problems (CVIPs) beyond the traditional inverse strongly monotone setting, focusing instead on a broader class of monotone and Lipschitz continuous operators. We introduce a novel two-step inertial algorithm incorporating self-adaptive regularization and relaxation techniques to address this generalized framework. We establish the strong convergence of the proposed method under mild assumptions. Extensive numerical experiments demonstrate that our algorithm consistently outperforms several existing approaches. Furthermore, we highlight the practical significance of our framework by reformulating a range of real-world applications, such as the elastic net in statistical learning, sparse logistic regression, and LASSO, as instances of CVIPs.

The following chemotaxis-consumption problem with no-flux boundary conditions has been considered

within a smoothly bounded domain (Omega subset mathbb{R}^{n}(ngeq 3)), where the parameters (kappa >beta >1), (alpha , gamma ,eta >0), and (T_{max }in (0,infty ]). This paper mainly examines the effects of nonlinear dissipation and nonlocal logistic feedback on solutions. Specifically, for all suitably regular initial data, it has been established that if

or

then the above system has a global classical solution. Compared with previous research results, the novelty (or difficulty) of this paper lies in the combination of non-local terms and nonlinear dissipation.

This paper is addressed to study asymptotic behavior for the Korteweg-de Vries equation with rapid oscillations, namely, the Korteweg-de Vries equation with rapidly oscillating potential and rapidly oscillating boundary force. In order to describe its asymptotic behavior, we establish the averaging principle for this system, this is important from both physical and mathematical standpoints. More precisely, two kinds of averaging principle is established, one is Bogoliubov first averaging principle for the Korteweg-de Vries equation on a finite time interval, the other is the Bogoliubov second averaging principle for the Korteweg-de Vries equation on the entire axis.

Exploring a more than 70 years old idea about the minimization of the spectral abscissa of linear functional differential equations, a series of recent works highlighted the insights that multiple spectral values may bring in the characterization of the decay rate for the solution of such dynamical systems. In fact, it has been shown that a spectral value of sufficiently high multiplicity tends to be dominant, in what is now known as the multiplicity-induced-dominancy (MID) property. When it is valid, this property can be remarkably helpful in the control of dynamical systems governed by functional differential equations or even some classes of partial differential equations. Beyond its simplicity, what sets it apart from other control methods is the valuable quantitative advantage it provides by prescribing the exact solution’s decay rate. Since then, many works have been dedicated to studying the extent of the MID as well as its use in practical control applications. In this paper, apart from the extension of the MID property to continuous-time difference functional equations with multiple delays, we study the case when the MID fails. In fact, despite the invalidity of the MID property, we emphasize the interest of forcing a spectral value multiplicity to derive a sharp estimate of the corresponding rightmost spectral value. To demonstrate the effectiveness of the proposed methodology, we consider the stabilization problem of the wave equation with an auto-regressive boundary feedback. By using an appropriate finite element modeling, a numerical simulation of the boundary control for the wave equation case is performed to illustrate these results through the example of vibration control of a long drill pipe submitted to a shock-like disturbance. The time responses show the effectiveness of the proposed approach and mainly that the decay rate can be arbitrarily selected.

This paper studies the asymptotic behavior of solutions to the non-autonomous Newton-Boussinesq equation defined on a two-dimensional unbounded Poincaré domain. Based on the well-posedness of solutions in (L^{2}(mathcal{O}) times L^{2}(mathcal{O})), we construct a continuous non-autonomous dynamical system in this space and prove the existence of a unique tempered pullback attractor. Moreover, under the assumption that the time-dependent external forces converge to time-independent fnctions as time approaches positive or negative infinity, we establish the asymptotically autonomous upper semicontinuity of the attractors. The main difficulty arising from the lack of compact Sobolev embeddings on unbounded domains is overcome by deriving uniform tail estimates for the solutions.