Work

On $ L^{\infty } $-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations

Year: 2024

Type: article

Abstract: In this paper, we study the structure of the global attractor for weak and regular solutions of a problem governed by a scalar semilinear reaction-diffusion 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^{\infty }(\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.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2024093

Authors: Rubén Caballero, Piotr Kalita, José Valero

Institutions: Jagiellonian University, Universitat de Miguel Hernández d'Elx

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403469735

FWCI:

Cites: 24

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Related to: 10