In the paper we consider nonlinear parabolic initial-boundary value problems with a discontinuous forcing term, which is locally of bounded variation. The existence of a maximal and a minimal solution, under the assumption that there exist an upper solution ' and a lower solution, is stated. Our approach is based on a Jordan-type decomposition for the discontinuous forcing term and on a fixed point theorem for nondecreasing maps in ordered Banach spaces.
Extremal solutions for nonlinear parabolic problems with discontinuities
CARDINALI, Tiziana;
1997
Abstract
In the paper we consider nonlinear parabolic initial-boundary value problems with a discontinuous forcing term, which is locally of bounded variation. The existence of a maximal and a minimal solution, under the assumption that there exist an upper solution ' and a lower solution, is stated. Our approach is based on a Jordan-type decomposition for the discontinuous forcing term and on a fixed point theorem for nondecreasing maps in ordered Banach spaces.File in questo prodotto:
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