Acta Applicandae Mathematicae最新文献

In this paper, the following cross-diffusion system is investigated

in a bounded domain (Omega subset mathbb{R}^{n}) ((nge 2)) with smooth boundary (partial Omega ). Under the condition that (alpha >frac{2n-mn-2}{2(n-1)}), (mgeq 1), and (beta leq frac{m+2}{2}), it is shown that the problem possesses a unique global bounded classical solution. Moreover, it is obtained that the corresponding solution exponentially converge to a constant stationary solution when the initial data (u_{0}) is sufficiently small.

A unique behaviour of the Schrödinger map equation, a geometric partial differential equation, is presented by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results are consistent with those for the vortex filament equation, an equivalent form of the Schrödinger map equation in the Euclidean space. Thus, with all possible choices of regular polygons in a given setting, our analysis not only provides a novel extension to its usefulness as a pseudorandom number generator but also complements the existing results.

This paper addresses a general nonhomogeneous incompressible cell-fluid Navier-Stokes model incorporating chemotaxis in a two or three-dimensional bounded domain. This model comprises two mass balance equations and two general momentum balance equations, specifically for the cell and fluid phases, combined with a convection-diffusion-reaction equation for oxygen. We establish the existence and uniqueness of a local strong solution under initial data that satisfy natural compatibility conditions. Additionally, we present a blow-up criterion for the strong solution.

We provide the well-posedness for a partially dissipative viscous system of balance laws in smooth Sobolev spaces under the same assumptions as in the case of inviscid balance laws. A priori estimates for coupled hyperbolic-parabolic linear systems with coefficients having limited regularity are derived using Friedrichs regularization and Moser-type estimates. Local existence for nonlinear systems will be established using the results of the linear theory and a suitable iteration scheme. The local existence theory is then applied to the Kuznetsov–Westervelt equation with damping for nonlinear wave acoustic propagation. Existence of global solutions for small data and their asymptotic stability are established.

We consider a system of two nonlocal and nonlinear partial differential equations that describe some aspects of yeast cell-cell communication. We study local and global existence and uniqueness of solutions. We consider mild solutions and we perform bilinear and trilinear fixed point arguments in suitable functional spaces.

This paper presents an inverse problem of identifying two ionic parameters of a nonlocal reaction-diffusion system in cardiac electrophysiology modelling. We used a nonlocal FitzHugh-Nagumo monodomain model which describes the electrical activity in cardiac tissue with the diffusion rate assumed to depend on the total electrical potential in the heart. We established at first, the global Carleman estimate adapted to nonlocal diffusion to obtain our main result which is the uniqueness and the Lipschitz stability estimate for two ionic parameters ((k,gamma )).

Stochastic ultimate boundedness has always been a very important property, which plays an important role in the study of stochastic models. Thus, in this paper, we will study a stochastic periodic chemostat system, in which we assume that the nutrient input concentration and noise intensities are periodic. In order to make the stochastic periodic model have mathematical and biological significance, we will study a very important issue: the existence, uniqueness and ultimate boundedness of a global positive solution for a stochastic periodic chemostat system.

For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.

In this article, we consider two- and three- dimensional stochastic convective Brinkman-Forchheimer extended Darcy (CBFeD) equations

on a torus, where (mu ,beta >0), (alpha in mathbb{R}), (rin [1,infty )) and (qin [1,r)). The goal is to show that the solutions of 2D and 3D stochastic CBFeD equations driven by Brownian motion can be approximated by 2D and 3D stochastic CBFeD equations forced by pure jump noise/random kicks on the state space (mathrm{D}([0,T];mathbb{H})). For the cases (d=2), (rin [1,infty )) and (d=3), (rin (3,infty )), by using minimal regularity assumptions on the noise coefficient, the results are established for any (mu ,beta >0). For the case (d=r=3), the same results are obtained for (2beta mu geq 1).

In this paper we study the existence of positive solutions for the following Schrödinger–Maxwell system of singular elliptic equations

where (Omega ) is a bounded open set of (mathbb{R}^{N}, N>2), (r>1), (0 < theta <1) and (f) is nonnegative function belongs to a suitable Lebesgue space. In particular, we take advantage of the coupling between the two equations of the system by proving how the structure of the system gives rise to a regularizing effect on the summability of the solutions.