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

共 50 条

[31] Interface development and local solutions to reaction-diffusion equations
Abdulla, UG
King, JR
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 32 (02) : 235 - 260
[32] On stability of nonhomogeneous periodic solutions to reaction-diffusion equations
Dikansky, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (01) : 181 - 185
[33] Global attractor and threshold dynamics of a reaction-diffusion population model in a polluted environment
Ma, An
Zhang, Qimin
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (01) : 989 - 1014
[34] Attractors for reaction-diffusion equations in RN with continuous nonlinearity
Morillas, F
Valero, J
ASYMPTOTIC ANALYSIS, 2005, 44 (1-2) : 111 - 130
[35] Global existence and blow-up solutions for quasilinear reaction-diffusion equations with a gradient term
Ding, Juntang
Guo, Bao-Zhu
APPLIED MATHEMATICS LETTERS, 2011, 24 (06) : 936 - 942
[36] ESTIMATES FOR A CLASS OF SLOWLY NON-DISSIPATIVE REACTION-DIFFUSION EQUATIONS
Pimentel, Edgard A.
Pimentel, Juliana F. S.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2016, 46 (03) : 1011 - 1028
[37] Weak upper semicontinuity of pullback attractors for nonautonomous reaction-diffusion equations
Simsen, Jacson
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2019, (68)
[38] Convergence of solutions of reaction-diffusion systems with time delays
Pao, CV
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 48 (03) : 349 - 362
[39] Trajectory attractor for a system of two reaction-diffusion equations with diffusion coefficient δ(t) → 0+ as t → + ∞
M. I. Vishik
V. V. Chepyzhov
Doklady Mathematics, 2010, 81 : 196 - 200
[40] Trajectory attractor for a reaction-diffusion system with a small diffusion coefficient
M. I. Vishik
V. V. Chepyzhov
Doklady Mathematics, 2009, 79 : 227 - 230

← 1 2 3 4 5 →