Acta Applicandae Mathematicae最新文献

In this article we investigate the approximate controllability results for delay fractional differential evolution systems with (psi )-Caputo fractional derivative. We derive sufficient conditions to establish the approximate controllability of the system with the help of the un-delayed corresponding system. Also the existence, uniqueness and boundedness of the mild solutions of the said systems are proved using Banach contraction principle. An example is provided at the end to validate the results.

The structural stability of Riemann solutions for a kind of Keyfitz-Kranzer (K-K) system with Chaplygin gas pressure and time-dependent source term is studied by the method of perturbation of initial value. It is rigorously proved that, as the perturbed parameter (varepsilon ) tends to zero, no mass concentration will happen even the initial perturbed density depends on (varepsilon ), which implies that the Riemann solutions of the K-K system are stable under the local small perturbation of the initial data.

In this paper, we design a new splitting method for solving nonmonotone inclusions in Hilbert spaces. Our method incorporates an inertial term, and a correction term into the forward-backward algorithm. The weak convergence of the sequence of iterations is derived, with worst-case rates of (o(k^{-1})) in terms of both the discrete velocity and the fixed point residual. The new method recovers the method in the literature as a special case. We also give some numerical experiments to demonstrate the efficiency of the proposed method.

We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.

This paper develops a new class of impulsive Atangana-Baleanu fractional stochastic differential systems with the Rosenblatt process, which is a Hermite process of order two with long-range dependence and stationary increments properties. Firstly, we established the existence of solutions to the considered problem by using the fixed point technique, resolvent family, and fractional calculus. Then, we discussed the controllability results for the proposed system. Finally, an illustrative example is given to demonstrate the obtained results.

In this work, a particular class of penalized Signorini’s models with a normal compliance contact condition is studied. These contact models are created by taking two parameters: a power parameter (alpha geq 1) and a punishment parameter (varepsilon ). A standard penalization is represented by a value of (alpha =1). These contact models function as nonlinear approximations for Signorini’s problem. Choosing a continuous, conforming linear finite element approximation is the first step in our method. We then calculate (L^{2})-error estimates with suitable assumptions, which are carefully examined and explained.

This paper concerns the Cauchy problem of the 3D magneto-viscoelastic fluids. Using the pure energy method, we prove the global well-posedness of the classical solutions with smooth initial data of small (L^{2}) energy. Furthermore, under some additional assumptions on the initial data, we obtain the algebraic temporal decay rates of the higher-order spatial derivatives of solutions.

In this paper, we study the convergence of the solutions to the Dirichlet problem of the incompressible micropolar fluid equations with full anisotropic dissipation toward the solution to the ideal micropolar fluid equations in the upper half-plane. By choosing suitable correctors, we find that if the vertical dissipation of horizontal fluid velocity, the vertical angular viscosity and the micro-rotation viscosity vanish more quickly than the others, the vanishing dissipation limit exists in (L^{infty }([0,T];L^{2}(mathbb{R}^{2}_{+}))). In addition, we deal with the difficulty caused by the micro-rotation viscosity. Further, we obtain the convergence rate.

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.