Louredo Aldo Trajano and Miranda Manuel Milla and Clark Marcondes R.: Variable exponent perturbation of a parabolic equation with p(x)-Laplacian. (2019)
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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: | 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: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/62284 |
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