AN INVESTIGATION OF NON-TRAPPING, ASYMPTOTICALLY EUCLIDEAN WAVE EQUATIONS Public Deposited

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  • March 19, 2019
Creator
  • Booth, Robert
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this dissertation, we demonstrate almost global existence for a class of variable coefficient, non-trapping, asymptotically Euclidean, quasilinear wave equations with small initial data. A novel feature is that the wave operator may be a large perturbation of the usual D'Alembertian operator. The key step is developing a local energy estimate for an appropriately linearized version of our wave equation. The linearized wave operator is a combination of a stationary, non-trapping, asymptotically Euclidean wave operator and a small time-dependent perturbation. The time-dependent perturbation need not be asymptotically Euclidean.
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Rights statement
  • In Copyright
Advisor
  • Marzuola, Jeremy
  • Taylor, Michael
  • Christianson, Hans
  • Canzani, Yaiza
  • Metcalfe, Jason
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2018
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