Semilinear parabolic equations involving measures and low regularity data
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- by H. Amann and P. Quittner PDF
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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.References
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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
- Received by editor(s): August 19, 2002
- Published electronically: September 22, 2003
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1984467