Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity

Year 2024, Volume: 53 Issue: 2, 367 - 381, 23.04.2024

Rabil Ayazoğlu Gülizar Alisoy Sezgin Akbulut Tuba Ağırman Aydın

https://doi.org/10.15672/hujms.1106985

Abstract

In this paper, we consider an initial boundary value problem for a class of $p(\cdot )$-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. By using new approach, we obtain the global and decay of existence of the solutions. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.

Keywords

parabolic, $p(\cdot )$-Laplacian, variable exponents, global existence, decay property, extinction

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