Acta Applicandae Mathematicae最新文献

This paper studies the Liouville type theorems for stationary the tropical climate model on the whole space (mathbb{R}^{3}). It shows that if ((u,v,theta )) satisfies certain anisotropic integrability conditions on the components of the (u) or ((u,v)), also (theta ) satisfies certain isotropic integrability conditions, there is only a trivial solution to the stationary tropical climate model. The results are a further extension of the recent work by Chae (Appl. Math. Lett. 142:108655, 2023).

In this article we address the problem of locating point forces within a time-dependent singular Brinkman flow. The context of the study is framed as an approximation of cerebrospinal fluid (CSF) around the central nervous system, with the point forces representing a model for the blood-brain barrier. We approach the problem by reformulating the identification task as an optimization problem, employing a tracking shape functional. A notable challenge in this study arises from the irregularity in the solution of the partial differential equation (PDE), which complicates the exploration of sensitivity analysis. To overcome this issue, we employ a relaxation method and compute the topological derivative of the cost function. The topological derivative, commonly used in shape optimization problems, offers insights into how the cost function responds to small perturbations in the domain. To determine the optimal position of the point forces, we employ a one-shot algorithm based on the derived topological gradient. Finally, we present numerical results that showcase the efficiency of our method in addressing the identified problem.

This paper investigates the fast chemical diffusion limit from a parabolic-parabolic Keller-Segel system to the corresponding parabolic-elliptic Keller-Segel system by constructing approximate solutions with an appropriate order via an asymptotic expansion. Nonlinear stability of the precise initial layer is characterized with an exact convergence rate by using basic energy method.

We investigate the following nonlinear bosonic equation on Euclidean space arising in string theory and cosmology:

where (nge 3), (m>0), (c>0) and (frac{f(x,u)}{u}) tends to a positive function (h(x)) independent of (u) as (urightarrow +infty ), (e^{-cDelta }) is given by a power series with (Delta ) is the Euclidean Laplace operator. Here, the nonlinear term (f(x,u)) does not satisfy the usual condition:

for (theta >0) and (|u|) is large, which is important in using the mountain pass theorem, see Alves et al. (J. Differ. Equ. 323:229-252, 2022) and Corrêa et al. (J. Differ. Equ. 363:491-517, 2023). This paper is devoted to discuss how to use the mountain pass theorem to obtain the existence of nontrivial solution to problem (P) without the (AR) condition.

This paper investigates the significance of employing random subgraphs and analyzing the expected values of Zagreb ndices within chemical graphs. By examining smaller, representative subsets, we uncover valuable insights into the properties and characteristics of complex networks. The expected values of Zagreb indices serve as critical mathematical measures for quantifying the structural complexity of chemical graphs, providing essential information about connectivity and branching patterns within molecules. Our primary contribution includes deriving theoretical expressions for these indices and validating them through extensive computational experiments on fullerene graphs (C_{20}) and (C_{60}). The results demonstrate that our theoretical predictions closely align with experimental findings, affirming the robustness of Zagreb indices in characterizing molecular structures. Additionally, our analysis of specific cases, such as complete graphs and complete bipartite graphs, is consistent with previous studies, further reinforcing our methodology. This research emphasizes the relevance of random subgraphs and expected values of Zagreb indices in advancing our understanding of molecular behavior and stability, with important implications for materials science and drug design.

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.