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Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential

Paschalis Karageorgis
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Abstract

We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time.

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Paschalis Karageorgis. 2005-03-09. Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential. https://arxiv.org/abs/math/0503171

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