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December  2010, 28(4): 1589-1601. doi: 10.3934/dcds.2010.28.1589

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, United States
2. 

Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, United States

Received  October 2009 Revised  February 2010 Published  June 2010

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.
Keywords: global existence, Wave equation, exterior domain..
Mathematics Subject Classification: Primary: 35L70, 35B40, 35L2.
Citation: Jason Metcalfe, Christopher D. Sogge. Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1589-1601. doi: 10.3934/dcds.2010.28.1589
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