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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 1, 1985, pp. 55–64
DOI: 10.4171/ZAA/137

Published online: 1985-02-28

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

Jörg Heinrich

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.

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Heinrich Jörg: Zur Lösbarkeit der Anfangs-Randwertaufgabe $\frac{\partial}{\partial t} u-D(x, t, u) \Delta u = f$ im Sobolew-Raum. Z. Anal. Anwend. 4 (1985), 55-64. doi: 10.4171/ZAA/137