In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
@article{bwmeta1.element.bwnjournal-article-div17i1-2n1bwm,
author = {N.U. Ahmed},
title = {Measure solutions for semilinear evolution equations with polynomial growth and their optimal control},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {17},
year = {1997},
pages = {5-27},
zbl = {0905.34056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div17i1-2n1bwm}
}
N.U. Ahmed. Measure solutions for semilinear evolution equations with polynomial growth and their optimal control. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 17 (1997) pp. 5-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div17i1-2n1bwm/
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