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January/February 2011 Global attractor for some wave equations of $p-$ and $p(x)-$Laplacian type
Nikolaos M. Stavrakakis, Athanasios N. Stylianou
Differential Integral Equations 24(1/2): 159-176 (January/February 2011). DOI: 10.57262/die/1356019049


We study the existence of solutions for the equation $u_{tt}-\Delta_{p(x)} u - \Delta u_{t} + g(u) = f(x,t), \; x \in \Omega$ (bounded) $ \subset \mathbb R^n, \; t>0$ in both the isotropic case $(p(x) \equiv p$, a constant) and the anisotropic case $(p(x)$ a measurable function). Furthermore, in the isotropic case we obtain results concerning the asymptotic behavior of solutions. Since uniqueness for this type of problem seems rather difficult, a method implementing generalized semiflows is being used to prove the existence of a global attractor in the phase space $W_0^{1,p}(\Omega)\times L^2(\Omega)$, when $p\geq n$.


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Nikolaos M. Stavrakakis. Athanasios N. Stylianou. "Global attractor for some wave equations of $p-$ and $p(x)-$Laplacian type." Differential Integral Equations 24 (1/2) 159 - 176, January/February 2011.


Published: January/February 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35056
MathSciNet: MR2759356
Digital Object Identifier: 10.57262/die/1356019049

Primary: 35B30 , 35B40 , 35B41 , 35B45 , 35L15 , 35L20 , 35L70 , 35L80

Rights: Copyright © 2011 Khayyam Publishing, Inc.

Vol.24 • No. 1/2 • January/February 2011
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