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

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

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