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Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge

Global Existence of Solutions to Multiple Speed Systems of Quasilinear Wave Equations in Exterior Domains

In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for systems of quasilinear wave equations with multiple speeds. The null condition only puts restrictions on the self-interactions of each wave family. We use the method of commuting vector fields and weighted space-time L² estimates.

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 17, 01/2005
Pages: 133 - 168

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