On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source |
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Authors: | Claudianor O Alves and Marcelo M Cavalcanti |
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Institution: | (1) Department of Mathematics and Statistics, Federal University of Campina Grande, 58109-970 Campina Grande, PB, Brazil;(2) Department of Mathematics, State University of Maringá, 87020-900 Maringá, PR, Brazil |
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Abstract: | This paper is concerned with the study of the nonlinear damped wave equation where Ω is a bounded domain of having a smooth boundary ∂Ω = Γ. Assuming that g is a function which admits an exponential growth at the infinity and, in addition, that h is a monotonic continuous increasing function with polynomial growth at the infinity, we prove both: global existence as
well as blow up of solutions in finite time, by taking the initial data inside the potential well. Moreover, optimal and uniform
decay rates of the energy are proved for global solutions.
The author is Supported by CNPq 300959/2005-2, CNPq/Universal 472281/2006-2 and CNPq/Casadinho 620025/2006-9.
Research of Marcelo M. Cavalcanti partially supported by the CNPq Grant 300631/2003-0. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35L05 35L20 35A07 |
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