Anvarbek Meirmanov, Sergey Shmarev
Abstract:
Let
be a regular domain and
be a given function.
If
is bounded
and the set
is bounded
in
,
then there is a sequence
such that
,
and
,
a.e. in
.
This assertion is applied to prove solvability
of the one-dimensional initial and boundary-value problem for a degenerate
parabolic equation arising in the Buckley-Leverett model of two-phase filtration.
We prove existence and uniqueness of a weak solution, establish the property
of finite speed of propagation and construct a self-similar solution.
Submitted September 25, 2014. Published October 27, 2014.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Compactness lemma; two-phase filtration; nonlinear PDE;
degenerate parabolic equations.
Show me the PDF file (271 KB), TEX file, and other files for this article.
Anvarbek Meirmanov Department of mahtematics, Belgorod State University ul.Pobedi 85, 308015 Belgorod, Russia email: anvarbek@list.ru | |
Sergey Shmarev Department of Mathematics, University of Oviedo c/Calvo Sotelo s/n, 33007, Oviedo, Spain email: shmarev@uniovi.es |
Return to the EJDE web page