Abstract and Applied Analysis
Volume 1 (1996), Issue 4, Pages 417-433
Flow invariance for perturbed nonlinear evolution equations
Fachbereich 17, Universität Paderborn, Paderborn D-33095, Germany
Received 22 November 1996
Copyright © 1996 Dieter Bothe. 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.
Let be a real Banach space, , an -accretive operator and continuous. In this paper we obtain necessary and sufficient conditions for weak positive invariance (also called viability) of closed sets for the evolution system
More generally, we provide conditions under which this evolution system has
mild solutions satisfying time-dependent constraints on . This result is then applied to obtain global solutions of reaction-diffusion systems with nonlinear diffusion, e.g. of type under certain assumptions on the set the function and .