On a nonolinear wave equation in unbounded domains

Carlos Frederico Vasconcellos

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

We study existence and uniqeness of the nonlinear wave equation ∂ 2 u ∂ t 2 + M ( x , ∫ | ∇ u ( x , t ) | 2 d x + ∫ | u ( x , t ) | 2 d x ) ( − Δ u + u ) = 0 in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:473020

DOI: 10.1155/S0161171288000390

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