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Existence of mild solutions for semilinear equation of evolution

Anna Karczewska, Stanisław Wędrychowicz (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize the set...

Global existence for a Riccati equation arising in a boundary control problem for distributed parameters

Franco Flandoli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.

Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

N.U. Ahmed (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

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