International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 79-102
Existence and decay of solutions of some nonlinear parabolic variational inequalities
1Department of Mathematics, College of General Education, Kyushu University, Fukuoka, Japan
2Department of Mathematical Sciences, Tokai University, Kanagawa, Japan
Received 23 January 1979
Copyright © 1980 Mitsuhiro Nakao and Takashi Narazaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper discusses the existence and decay of solutions of the variational inequality of parabolic type: for with a.e. in , where is a closed convex set of a separable uniformly convex Banach space , is a nonlinear monotone operator from to and is a nonlinear operator from Banach space to . and are related as for a Hilbert space . No monotonicity assumption is made on .