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On the Unbounded Behavior for Some Non-autonomous Systems in Banach Spaces

✍ Scribed by B.D. Rouhani

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 445 KB
Volume: 110
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1994.1068

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✦ Synopsis

By modifying our previous methods (1992, J. Nonlinear Anal. TMA 19, 741-751; 1993, Proc. Amer. Math. Soc. 117, 951-956), and by using the notion of integral solution introduced by Ph. Bénilan (1972, "Equations d'évolution dans un espace de Banach quelconque et applications," thesis, Université Paris XI, Orsay), we study the asymptotic behaviour of unbounded trajectories for the quasiautonomous dissipative system (d u / d t+A u \ni f), where (X) is a real Banach space, (A) an accretive (possibly multivalued) operator in (X \times X), and (f-f_{x} \in L^{p}((0,+\infty) ; X)) for some (f_{x} \in X) and (1 \leqslant p<\infty). 1994 Academic Press, Inc.

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