Attractors for parabolic problems with p(x)-Laplacian: Bounds, continuity of the flow and robustness

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Author(s):	Carvalho, Alexandre N. ; Simsen, Jacson ; Simsen, Mariza S. Total Authors: 3
Document type:	Journal article
Source:	Journal of Mathematical Analysis and Applications; v. 547, n. 1, p. 30-pg., 2025-01-22.
Abstract
In this work we consider a family of quasilinear equations with variable exponents (p(x)-Laplacian) and perturbations which are not globally Lipschitz. We prove existence of global solutions, existence of global attractors and we provide conditions on the data in order that the associated semilinear equation (p(x) equivalent to 2) commands the asymptotic dynamics of the family of problems when the exponents are sufficiently close to 2 (uniformly in x ) by showing the continuity of the flows and the upper semicontinuity of the global attractors. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

FAPESP's process:	20/14075-6 - Dynamical systems and their attractors under perturbations
Grantee:	Alexandre Nolasco de Carvalho
Support Opportunities:	Research Projects - Thematic Grants