Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 198, pp. 117.
Entropy solutions for nonlinear degenerate ellipticparabolichyperbolic
problems
Ning Su, Li Zhang
Abstract:
We consider the nonlinear degenerate ellipticparabolichyperbolic equation
where g and b are nondecreasing continuous functions,
is vectorial and continuous, and f is Lipschitz continuous.
We prove the existence, comparison and uniqueness of entropy solutions
for the associated initialboundaryvalue problem where
is a
bounded domain in
.
For the associated initialvalue problem where
,
,
the existence of entropy solutions is proved.
Moreover, for the case when
is locally Holder continuous
of order
,
and
,
where
is nondecreasing continuous with
,
we can prove the
contraction
principle, and hence the uniqueness.
Submitted December 6, 2013. Published September 23, 2014.
Math Subject Classifications: 35J70, 35K65, 35L80.
Key Words: Nonlinear evolution equation; degenerate equation; entropy solution;
existence; uniqueness.
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Ning Su
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China
email: nsu@math.tsinghua.edu.cn


Li Zhang
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China
email: zhli25@163.com

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