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 .
"Qualitative Properties of Nonnegative Solutions for a Doubly Nonlinear Problem with Variable Exponents." Abstr. Appl. Anal. 2018 1 - 14, 2018. https://doi.org/10.1155/2018/3821217