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Blow-up and critical exponents for nonlinear hyperbolic equations

โœ Scribed by V.A. Galaktionov; S.I. Pohozaev

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
159 KB
Volume
53
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

We prove nonexistence results for the Cauchy problem for the abstract hyperbolic equation in a Banach space X ,

where f : X โ†’ R is a C 1 -function. Several applications to the second-and higher-order hyperbolic equations with local and nonlocal nonlinearities are presented. We also describe an approach to Kato's and John's critical exponents for the semilinear equations ut = u + b(x; t)|u| p ; p ยฟ 1, which are responsible for phenomena of stability, unstability, blow-up and asymptotic behaviour.

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โœ Fuqin Sun; Mingxin Wang ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 224 KB

In this paper, we study a nonlinear hyperbolic system with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of weak solution. Secondly, via some inequalities, applying the potential method and the