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

Mitsuhiro Nakao1 and Takashi Narazaki2

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 u(t) of the variational inequality of parabolic type: <u(t)+Au(t)+Bu(t)f(t),v(t)u(t)>0for vLp([0,);V)(p2) with v(t)K a.e. in [0,), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as VWH for a Hilbert space H. No monotonicity assumption is made on B.