Variable exponent perturbation of a parabolic equation with p(x)-Laplacian

Louredo, Aldo Trajano and Miranda, Manuel Milla and Clark, Marcondes R.: Variable exponent perturbation of a parabolic equation with p(x)-Laplacian.

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Abstract

This paper is concerned with the study of the global existence and the decay of solutions of an evolution problem driven by an anisotropic operator and a nonlinear perturbation, both of them having a variable exponent. Because the nonlinear perturbation leads to difficulties in obtaining a priori estimates in the energy method, we had to significantly modify the Tartar method. As a result, we could prove the existence of global solutions at least for small initial data. The decay of the energy is derived by using a differential inequality and applying a non-standard approach.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 60
ISSN: 1417-3875
Page Range: pp. 1-14
DOI: https://doi.org/10.14232/ejqtde.2019.1.60
Uncontrolled Keywords: Laplace-egyenlet, Differenciálegyenlet
Additional Information: Bibliogr.: p. 13-14. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 30. 10:06
Last Modified: 2020. Jul. 29. 12:24
URI: http://acta.bibl.u-szeged.hu/id/eprint/62284

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