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.