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Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent

โœ Scribed by Toundykov, Daniel; Lasiecka, Irena; Chueshov, Igor

Book ID
126993408
Publisher
American Institute of Mathematical Sciences
Year
2008
Tongue
English
Weight
63 KB
Volume
20
Category
Article
ISSN
1078-0947

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We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la