ON L∞-ESTIMATES AND THE STRUCTURE OF THE GLOBAL ATTRACTOR FOR WEAK SOLUTIONS OF REACTION-DIFFUSION EQUATIONS

被引：0

作者：

Caballero, Ruben ^{[1
]}

Kalita, Piotr ^{[2
]}

Valero, Jose ^{[1
]}

机构：

[1] Univ Miguel Hernandez Elche, Ctr Invest Operat, Ave Univ s-n, Elche 03202, Spain

[2] Jagiellonian Univ, Fac Math & Comp Sci, ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2025年 / 24卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Reaction-diffusion equations; set-valued dynamical system; global at- tractor; unstable manifolds; asymptotic behavior; REGULARITY; SYSTEMS;

D O I：

10.3934/cpaa.2024093

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. In this paper, we study the structure of the global attractor for weak and regular solutions of a problem governed by a scalar semilinear reactiondiffusion equation with a non-regular nonlinearity, such that uniqueness of solutions can fail to happen. First, using the Moser-Alikakos iterations we obtain the estimates of the weak solutions in the space L infinity (Omega). After that, using these estimates we improve the existing results on the structure of the attractor. Finally, estimates of the Hausdorff and fractal dimension of the attractor are obtained.

引用

页码：365 / 388

页数：24

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