Huashui Zhan
Abstract:
We introduce a new type of the weak solution of the polytropic
filtration equations with a convection term,
Here,
is a domain with a
smooth boundary
,
,
,
,
,
when
and
when
. Since the equation is degenerate on
the boundary, its weak solutions may lack the needed regularity to have a
trace on the boundary. The main aim of the paper is to establish the
stability of the weak solution without any boundary value condition.
Submitted February 16, 2017. Published September 8, 2017.
Math Subject Classifications: 35L65, 35K85, 35R35.
Key Words: Polytropic filtration equation; convection term; stability;
boundary value condition.
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Huashui Zhan School of Applied Mathematics Xiamen University of Technology Xiamen, Fujian 361024, China email: 2012111007@xmut.edu.cn |
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