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Zbl 1072.35094
Amann, H.; Quittner, P.
Semilinear parabolic equations involving measures and low regularity data. (English)
[J] Trans. Am. Math. Soc. 356, No. 3, 1045-1119 (2004). ISSN 0002-9947; ISSN 1088-6850/e

This paper generalizes considerably earlier investigations of the authors, constituting the first systematic and detailed study of abstract parabolic evolution equations involving measures that depend nonlinearly on the solution. These measures can be initial, Neumann, or Dirichlet data, or e. g. represent flow across a moving membrane, or a number of moving point sources located in the interior of the domain of existence. In some situations the theory applies for distributions more singular than measures.\par The paper contains a number of existence and continuous dependence on data results (in suitable spaces), and a collection of examples illustrating how the theory applies. The methods used stem from semigroup theory and functional analysis.
[Marianne Korten (Manhattan)]

MSC 2000:: *35K60 (Nonlinear) BVP for (non)linear parabolic equations
35K90 Abstract parabolic evolution equations
35R05 PDE with discontinuous coefficients or data

Keywords: semilinear parabolic equations and systems; measure and singular boundary and initial data; semigroup methods; continuous dependence on data; semigroup theory

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