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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.
Additional information
Funding
The project is supported by NSFC [11271154], by Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 program of Jilin University. The first author is also supported by Graduate Innovation Fund of Jilin University. The second author is also supported by Fundamental Research Funds of Jilin University (450060501179).