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On the Boundedness of Global Solutions of Abstract Semilinear Parabolic Equations

โœ Scribed by Marek Fila; Howard A. Levine

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
213 KB
Volume
216
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

In this paper we consider the question of the long time behavior of solutions of ลฝ . the initial value problem for evolution equations of the form durdt q Au t s ลฝ ลฝ .. F u t in a Banach space where A is the infinitesimal generator of an analytic semigroup and F is a nonlinear function such that the initial value problem possesses nonglobal solutions for some initial data. We give sufficient conditions to w w .x ensure that global solutions on 0, ฯฑ are necessarily bounded in a suitable norm. We give several examples of problems to which the abstract result applies. แฎŠ 1997

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