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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Pages 000­000
S 0002-9947(XX)0000-0
SEMILINEAR PARABOLIC EQUATIONS INVOLVING
MEASURES AND LOW REGULARITY DATA
H. AMANN AND P. QUITTNER
Abstract. A detailed study of abstract semilinear evolution equations of the
form u + Au = µ(u) is undertaken, where -A generates an analytic semigroup
and µ(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 para-
bolic 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.
Introduction
In this paper we extend the theory of linear parabolic evolution problems in-
volving measures, developed in [5], to the case of semilinear evolution equations of
the form
u + Au = µ(u) in [0, T], (0.1)

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics