Acta Applicandae Mathematicae最新文献

This paper is dedicated to the long-time behavior of a system of coupled one-dimensional wave equations modeling helicoidal flows of Maxwell fluid. In a scenario featuring nonlinear damping and source terms of arbitrary polynomial growth, we prove the existence of smooth finite dimensional global attractors as well as exponential attractors. We also prove that its long-time dynamics is completely determined by a finite set of linear continuous functionals.

In this paper, we study a quantitative refinement of a classical symmetrisation result for first-order Hamilton-Jacobi equations. We prove that the deficit in the comparison result, established by Giarrusso and Nunziante, controls both the asymmetry of the domain and the deviation of the solution and data from radial symmetry. This yields a stability version of the Giarrusso-Nunziante inequality.

In this paper, we apply Picard’s method to solve fractal differential equations arising in both ordinary and partial forms. We begin with a brief review of fractal calculus and introduce the Fractal Picard Iteration Method. This method is then used to solve ordinary and partial fractal differential equations systematically. As applications, we demonstrate the effectiveness of the approach by solving the fractal model of an RL circuit and the Schrödinger equation for a free particle. The results highlight the adaptability and strength of Picard’s method in addressing problems within fractal frameworks.

This paper investigates a contact and friction problem involving two electro-elastic bodies that interact with an electrically conductive foundation. The proposed model incorporates Signorini contact conditions with friction, non-homogeneous Neumann boundary conditions for non-contact zones and Robin boundary conditions for mechanical displacement. The resulting weak variational formulation is a system of nonlinear quasi-variational inequality and variational equality. The existence of solutions is established using fixed-point theory, and uniqueness is guaranteed under a smallness condition that relates the mechanical and electrical properties.

In this paper, we study a population dynamics model containing one prey and two predators, combining the Smith growth model, the Holling Type II, and the Monod-Haldane functional response. We introduce time lags, nonlinear suppression terms, and Allee effects. We demonstrate the persistence of the system, showing that under specific parameter conditions, the system is able to maintain the population size within positive values and finite intervals. We also prove the global asymptotic stability of the system near the internal equilibrium point and investigate the effect of the time lag parameter on the stability of the system, which shows that the system will change from steady state to periodic oscillation when the time lag parameter exceeds a certain critical value. In the sensitivity analysis section, we develop the study using two approaches: firstly, the direct method reveals that the system shows high sensitivity to small changes in the time lag parameter in the early stage; and then, by combining the Latin Hypercubic Sampling (LHS) method and the Partial Correlation Coefficients (PRCC), we conduct global uncertainty and sensitivity analyses of the parameters in the system in order to assess the effect of different parameters on the model output. Numerical simulations validate our theoretical derivations and demonstrate the complex behavioral patterns of the system under different time lag conditions. This study provides an important theoretical basis for understanding predator-prey dynamics and suggests a strong methodological support for biodiversity conservation and ecosystem management.

This paper is devoted to the study of a class of reaction diffusion difference systems with distributed delay and a non monotone nonlinearity admitting three equilibria, those types of nonlinearities are famously known as bistable nonlinearities. We describe the asymptotic behaviour of solutions of such problems, and we prove that according to the initial data, the trivial and the second steady state are attractive. This implies naturally that the first steady state is not stable. The fact that the nonlinearity is not monotone makes it difficult to use a direct sub-and supersolution argument, therefore we adapt an adequate method. To our knowledge, this is the first time where such types of general systems are studied.

This work presents a comprehensive efficiency and convergence analysis of wavelet-based methods within a multi-dimensional framework for detecting singularities in nonlocal weakly singular integro-partial differential equations in one and two dimensions. The proposed approach incorporates the multi-resolution properties of wavelets to accurately identify and localize singularities in solutions to such equations. Combinations of space-time wavelets with their advantages are very limited for higher-dimensional problems, and their convergence analysis on collocation points is not fully clear till the present day. For problems having time singularity, the present work shows that multi-resolution analysis through 2D/3D Haar wavelets requires a lower regularity assumption for the convergence of the proposed procedure than several approaches on finite-difference setup or other wavelets like Hermite, Chebyshev, or Bernoulli’s wavelets. In particular, we produce a higher-order convergence result (second-order accurate) in the (L^{2}) norm, based on sufficient regularity assumptions on the solution. In addition to the higher-order estimate, we provide the wavelet-based truncation error estimate for several terms, such as the time-fractional derivative, Volterra & Fredholm integral operators, classical derivatives, and their effects on the regularity of the function for future researchers in this domain. Numerical tests are performed in the (L^{2}) and (L^{infty }) norms to compare the efficiency of this method over existing approaches for weakly singular nonlocal integro-partial differential equations. These experiments show the efficiency of the proposed approach in several kinds of regularity assumptions of the solution. This also guarantees the convergence of approximations to the functions having weak singularities in time and the higher-order accuracy for sufficiently smooth solutions.

In this paper, we investigate the primitive three-dimensional dynamic equations for moist atmosphere with only horizontal dissipation. Especially, we introduce the phase transformation of water vapor, which are considered as some nonlinear functions related to temperature and pressure. For any (H^{1}) initial data, the local well-posedness of strong solution can be established by decomposing velocity field into barotropic velocity field and baroclinic velocity field, as well as energy estimates method. Furthermore, applying logarithmic type Sobolev inequality, we can obtain the estimates of state functions in global time. Then the well-posedness of global strong solution can be proved.

In this study, we delve into the dynamics of plant, pollinator, and herbivore interactions using fractional models, which effectively capture memory effects and intricate temporal dependencies that conventional integer-order models often overlook. A significant result is the numerical evidence of oscillatory dynamics induced by variations in the predator mortality parameter. Our findings reveal that the dynamics and stability of the system depend on the fractional order. In the classical case, a Hopf bifurcation emerges, accompanied by a limit cycle, in agreement with the existing literature. Moreover, analysis across different fractional orders shows similar behavior when a pair of complex eigenvalues crosses the Matignon sector, inducing a change in the equilibrium’s stability and producing oscillatory patterns. These insights offer valuable information on the parameters that drive ecosystem dynamics and contribute to a more comprehensive understanding of fractional system stability in ecological modeling.

The purpose of this paper is to study the incompressible MHD equations with vertical magnetic diffusion in (mathbb{R}^{3}). We establish the global well-posedness of the system if the initial data are axially symmetric and the swirl component of the initial velocity is sufficiently small.