Transactions of the American Mathematical Society

Author(s): H. Amann; P. Quittner
Journal: Trans. Amer. Math. Soc. 356 (2004), 1045-1119.
MSC (2000): Primary 35K55, 35K60, 35K90, 28B05
Posted: September 22, 2003
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Abstract: A detailed study of abstract semilinear evolution equations of the form $\dot u+Au=\mu(u)$ is undertaken, where

generates an analytic semigroup and $\mu(u)$ is a Banach space valued measure depending on the solution. Then it is shown that the general theorems apply to a variety of semilinear parabolic boundary value problems involving measures in the interior and on the boundary of the domain. These results extend far beyond the known results in this field. A particularly new feature is the fact that the measures may depend nonlinearly and possibly nonlocally on the solution.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35K55, 35K60, 35K90, 28B05

H. Amann
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH--8057 Zürich, Switzerland
Email: amann@math.unizh.ch

P. Quittner
Affiliation: Institute of Applied Mathematics, Comenius University, SK--84248 Bratislava, Slovakia
Email: quittner@fmph.uniba.sk

DOI: 10.1090/S0002-9947-03-03440-8
PII: S 0002-9947(03)03440-8
Keywords: Nonlinear parabolic systems, weak solutions, measure data, critical exponents
Received by editor(s): August 19, 2002
Posted: September 22, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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