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Nonlinear analytic semiflows*

Published online by Cambridge University Press:  14 November 2011

Sigurd B. Angenent
Sigurd B. Angenent
Affiliation:
Department of Mathematics, University of Wisconsin at Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, U.S.A.
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Synopsis

In this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems (x′(t) = f(x(t))), and quasilinear initial value problems (x′(t)=A(x(t))x(t) + f(x(t))). This theory extends the theory of DaPrato and Grisvard of 1979, and shows how various properties, like analyticity of solutions, can be derived as a direct corollary of the existence theorem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 1-2 , 1990 , pp. 91 - 107
Copyright
Copyright © Royal Society of Edinburgh 1990

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