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May  2007, 19(2): 335-359. doi: 10.3934/dcds.2007.19.335

Elliptic-parabolic variational inequalities with time-dependent constraints

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

Received  August 2005 Revised  September 2006 Published  July 2007

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.
Citation: Masahiro Kubo, Noriaki Yamazaki. Elliptic-parabolic variational inequalities with time-dependent constraints. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 335-359. doi: 10.3934/dcds.2007.19.335
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