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2005 Quasilinear parabolic problems via maximal regularity
Herbert Amann
Adv. Differential Equations 10(10): 1081-1110 (2005).

Abstract

We use maximal $L_p$~regularity to study quasilinear parabolic evolution equations. In contrast to all previous work we only assume that the nonlinearities are defined on the space in which the solution is sought for. It is shown that there exists a unique maximal solution depending continuously on all data, and criteria for global existence are given as well. These general results possess numerous applications, some of which will be discussed in separate publications.

Citation

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Herbert Amann. "Quasilinear parabolic problems via maximal regularity." Adv. Differential Equations 10 (10) 1081 - 1110, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1103.35059
MathSciNet: MR2162362

Subjects:
Primary: 34G20
Secondary: 35B35, 35K90, 47H20, 47N20

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 10 • 2005
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