Abstract
This paper is concerned with the finite time extinction of solutions to a fast diffusive polytropic filtration system , with homogeneous Dirichlet boundary conditions in a bounded domain for any . It is shown that if , then any solution of this problem vanishes in finite time when the initial data are “comparable”; if and is suitably small, then there exists a solution that vanishes in finite time for small initial data. On the other hand, when , , and , which is a special case of , there exists at least one non-extinction solution for any positive smooth initial data.
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