The sharp lifespan for quasilinear wave equations in exterior domains with polynomial local energy decay

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  • March 20, 2019
Creator
  • Helms, John Albert
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • We investigate the lifespan of quasilinear Dirichlet-wave equations of the form (lower case delta squared subscript t - Delta) u = Q(u,u prime,u prime prime) in [0,T] times R superscript3 backslash K, where K is a bounded domain with smooth boundary. Previous results have demonstrated long time existence in the case that K was assumed to be star-shaped. We show that the same lifespan holds for more general geometries, where we only assume a polynomial local decay of energy with a possible loss of regularity for solutions to the linear homogeneous wave equation.
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  • In Copyright
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  • ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics.
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  • Metcalfe, Jason
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