Global Existence and Blow‐Up of Solutions for Nonlinear Klein‐Gordon Equation with Damping Term and Nonnegative Potentials

Wen-Yi Huang and Wen-Li Chen

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: This paper is concerned with the nonlinear Klein‐Gordon equation with damping term and nonnegative potentials. We introduce a family of potential wells and discuss the invariant sets and vacuum isolating behavior of solutions. Using the potential well argument, we obtain a new existence theorem of global solutions and a blow‐up result for solutions in finite time.

Date: 2014
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https://doi.org/10.1155/2014/142892

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:142892

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