Abstract
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 .
Citation
Dieter Bothe. "Flow invariance for perturbed nonlinear evolution equations." Abstr. Appl. Anal. 1 (4) 417 - 433, 1996. https://doi.org/10.1155/S1085337596000231
Information