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Transactions of the American Mathematical Society

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Semilinear parabolic equations involving measures and low regularity data


Authors: H. Amann and P. Quittner
Journal: Trans. Amer. Math. Soc. 356 (2004), 1045-1119
MSC (2000): Primary 35K55, 35K60, 35K90, 28B05
DOI: https://doi.org/10.1090/S0002-9947-03-03440-8
Published electronically: September 22, 2003
MathSciNet review: 1984467
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Abstract: A detailed study of abstract semilinear evolution equations of the form $\dot u+Au=\mu(u)$ is undertaken, where $-A$ 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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Additional Information

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: https://doi.org/10.1090/S0002-9947-03-03440-8
Keywords: Nonlinear parabolic systems, weak solutions, measure data, critical exponents
Received by editor(s): August 19, 2002
Published electronically: September 22, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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