Semilinear parabolic equations involving measures and low regularity data

Amann, H.; Quittner, P.

doi:10.1090/S0002-9947-03-03440-8

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ISSN 1088-6850(online) ISSN 0002-9947(print)

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
Posted: September 22, 2003
MathSciNet review: 1984467
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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