Global existence for high dimensional quasilinear wave equationsexterior to star-shaped obstacles

Jason Metcalfe; Christopher D. Sogge

doi:10.3934/dcds.2010.28.1589

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2010, Volume 28, Issue 4: 1589-1601. Doi: 10.3934/dcds.2010.28.1589

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Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles

Jason Metcalfe^1, and
Christopher D. Sogge^2,

1.
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250
2.
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218

Received: September 30, 2009

Revised: January 31, 2010

Published: November 2010

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Abstract

We prove global existence for quasilinear wave equations in high dimensional exterior domains with Dirichlet boundary conditions. In particular, we permit the nonlinear term to depend on the solution, not just its first and second derivatives. The key estimates are variants on localized energy estimates.

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Mathematics Subject Classification: Primary: 35L70, 35B40, 35L20.

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