Acta Applicandae Mathematicae最新文献

This article focuses on inverse problem for Hallaire-Luikov moisture transfer equation involving Hilfer fractional derivative in time. Hallaire-Luikov equation is used to study heat and mass transfer in capillary-porous bodies. Spectral expansion method is used to find the solution of the inverse problem. By imposing certain conditions on the functions involved and utilizing certain properties of multinomial Mittag-Leffler function, it is shown that the solution to the equation, known as the inverse problem, is regular and unique. Moreover, the inverse problem exhibits ill-posedness in the sense of Hadamard. The article ends with an example to demonstrate these theoretical findings.

In this paper, we consider a Lotka-Volterra competition-diffusion system with resource-dependent dispersal. We study the linear v.s. global asymptotic stability of steady states. Furthermore, how the diffusion coefficients and the dispersal strategies of two competing species affect the stability of steady states are given. This paper is a further study of (Tang and Wang in J. Math. Biol. 86:23, 2023).

For a super Korteweg-de Vries (KdV) equation introduced by Geng and Wu, nonlocal infinitesimal symmetries depending on eigenfunctions of its (adjoint) linear spectral problem are constructed from gradient of the spectral parameter, and one of such symmetries is shown to be related to a nonlocal infinitesimal symmetry of Kupershmidt’s super modified KdV equation via a Miura-type transformation. On this basis, a finite symmetry transformation is established for an enlarged system, and leads to a non-trivial exact solution and a Bäcklund transformation of Geng-Wu’s super KdV equation. A procedure is explained to generate infinitely many conservation laws. Moreover, these results could be reduced to classical situations, and their bosonic limits are briefly summarized.

In this note, we study numerically the regularity issue of the ideal MHD equations on the two-dimensional torus. By pseudo-spectral method, we provide evidence that a certain numerical solution is initially regular and eventually very singular in finite time.

In this paper, we study a Kirchhoff-type problem driven by a multi-phase operator with three variable exponents. Such problem has a right-hand side consisting of a Carathéodory perturbation which is defined only locally as well as the Kirchhoff term. Using a generalized version of the symmetric mountain pass theorem along with recent a priori upper bounds for multi-phase problems, we get whole a sequence of nontrivial solutions for our problem converging to zero in the appropriate Musielak-Orlicz Sobolev space and in (L^{infty }(Omega )).

Difference equations play a crucial role in a wide array of mathematical and physical tasks. In this article, we focus on the analysis of a second order linear homogeneous difference equation with smooth coefficients via WKB method. It is well-known that such equations exhibit two WKB solutions in a segment devoid of turning and singular points. We establish a theorem demonstrating the existence of these solutions in an unbounded domain under certain conditions regarding the smoothness and growth behavior of the coefficients at infinity. Furthermore, using this theorem, we derive the asymptotic expansion of Laguerre polynomials for large orders and values, yielding estimates that align with existing results.

This paper addresses the existence and exponential stability problem of highly nonlinear hybrid neutral pantograph stochastic equations with multiple delays (HNPSDEswMD). By Lyapunov functional method and without laying down a linear growth condition, the above problem of the exact solution is shown. We end up with two numerical examples that corroborates our theoretical findings.

In the present paper, we consider a mathematical model describing the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. We employ the nonlinear constitutive viscoelastic law with long-term memory and thermal effects. We describe some contact and thermal conditions with the Clarke subdifferential boundary conditions. We derive the weak formulation of the problem as a system coupling two variational-hemivariational inequalities. We provide results on the existence and uniqueness of a weak solution to the model by using recent results from the theory of variational-hemivariational inequalities. Finally, the continuous dependence of the solution on the data is derived by applying an abstract result that we demonstrate.

Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods with a convergence order of about 2.4142 and one method without memory with third-order convergence are devised using both Taylor’s expansion and the backward difference operator. We provide an extensive analysis of local and semilocal convergence. We also use polynomiography to analyze the methods visually. Finally, the proposed iterative approaches outperform a number of existing memory-based methods when applied to one-dimensional nonlinear models taken from different fields of science and engineering.

In this paper, we establish preservation properties of relative aging orders under distorted distributions. The relative hazard rate order and the relative reversed hazard rate order are considered. Using the derived results, a preservation property of the relative hazard rate order and a preservation property of the relative reversed hazard rate order derived perviously by Misra and Francis (Stat. Probab. Lett. 106:272–280, 2015) for, respectively, parallel and series systems are strengthened. Examples are also presented to illustrate the applicability of the obtained results.