Semilinear parabolic equations involving measures and low regularity data

Amann, H.; Quittner, P.

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

Semilinear parabolic equations involving measures and low regularity data
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by H. Amann and P. Quittner PDF

Trans. Amer. Math. Soc. 356 (2004), 1045-1119 Request permission

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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