On the global existence and extinction behavior for a polytropic filtration equation with variable coefficients

Abstract

<abstract><p>This article is devoted to the global existence and extinction behavior of the weak solution to an inhomogeneous polytropic filtration equation. Based on the integral norm estimate approach, the conditions on the global existence and the occurrence of the extinction singularity of the weak solution are given. Moreover, we also prove the non-extinction result under some appropriate assumptions by using the weak upper and lower solutions method.</p></abstract>