Elliptic-parabolic variational inequalities with time-dependent constraints

Masahiro Kubo; Noriaki Yamazaki

doi:10.3934/dcds.2007.19.335

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2007, Volume 19, Issue 2: 335-359. Doi: 10.3934/dcds.2007.19.335

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Elliptic-parabolic variational inequalities with time-dependent constraints

Masahiro Kubo^1, and
Noriaki Yamazaki^2,

1.
Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555
2.
Department of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-chō, Muroran

Received: July 31, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

We study variational inequalities for quasilinear elliptic-parabolic equations with time-dependent constraints. Introducing a general condition for the time-dependence of convex sets defining the constraints, we establish theorems concerning existence, uniqueness as well as an order property of solutions. Some applications of the general results are given.

Keywords:

Elliptic-parabolic variational inequalities,
flows in porous media,
nonlinear evolution equations.

Mathematics Subject Classification: Primary: 35K85, 35K65; Secondary 47J35, 76S05.

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