Variable exponent perturbation of a parabolic equation with p(x)-Laplacian
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 es...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Laplace-egyenlet, Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.60 |
| Online Access: | http://acta.bibl.u-szeged.hu/62284 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-14 |
| ISSN: | 1417-3875 |