Zur Lösbarkeit der Anfangs-Randwertaufgabe $\frac{\partial }{\partial t}u-D(x,t,u)\Delta u=f$ im Sobolew-Raum

Abstract

The subject of this paper is a quasilinear parabolic initial-boundary-value problem for functions with values in an arbitrary Hilbert-space. The results of a previous paper permit a simple approach. We transfer the problem into a fixed point problem, which we can solve with the help of a well-known fixed point theorem.