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Qualitative Properties of Nonnegative Solutions for a Doubly Nonlinear Problem with Variable Exponents

Zakariya Chaouai () and Abderrahmane El Hachimi ()

Abstract and Applied Analysis, 2018, vol. 2018, 1-14

Abstract: We consider the Dirichlet initial boundary value problem , where the exponents , , and are given functions. We assume that is a bounded function. The aim of this paper is to deal with some qualitative properties of the solutions. Firstly, we prove that if , then any weak solution will be extinct in finite time when the initial data is small enough. Otherwise, when , we get the positivity of solutions for large . In the second part, we investigate the property of propagation from the initial data. For this purpose, we give a precise estimation of the support of the solution under the conditions that and either or a.e. Finally, we give a uniform localization of the support of solutions for all , in the case where a.e. and .

Date: 2018
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DOI: 10.1155/2018/3821217

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