arXiv:1003.4760 Abstract | arXiv Analytics

arXiv:1003.4760 [math.AP]Abstract References Reviews Resources

Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

Published 2010-03-24, updated 2012-02-27Version 3

In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then it is proved that this global attractor is a bounded subset of H^{2}(\Omega)\times H^{2}(\Omega) and also a global attractor in H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega).

Categories: math.AP, math.DS

Subjects: 35B41, 35L05, 35L75

Keywords: strongly damped wave equation, global attractor, nonlinear source term, displacement dependent damping, critical exponent

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