arXiv:math/0404420 Abstract

arXiv:math/0404420 [math.AP]Abstract References Reviews Resources

Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions

Published 2004-04-22, updated 2005-04-08Version 2

We prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions four and higher. This generalizes a result of Shibata and Tsutsumi in spatial dimensions greater than or equal to six. The technique of proof would allow for more complicated geometries provided that an appropriate local energy decay exists for the associated linear wave equation.

Comments: Some corrections (per the referee's suggestions) were made in Section 3. 24 pages

Categories: math.AP

Subjects: 35L70, 42B99

Keywords: global existence, dirichlet-wave equations, quadratic nonlinearties, high dimensions, appropriate local energy decay

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