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arXiv:math/0503171 [math.AP]AbstractReferencesReviewsResources

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

Paschalis Karageorgis

Published 2005-03-09Version 1

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.

Comments: 34 pages, 1 figure
Categories: math.AP
Subjects: 35C15, 35L05, 35L15
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