Nonlinear Geometric Optics for Reflecting and Evanescent Pulses Public Deposited

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Last Modified
  • March 19, 2019
Creator
  • Willig, Colton
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • Weakly nonlinear geometric optics expansions of highly oscillatory reflecting and evanescent pulses are considered for a general class of differential operators. Through rigorous error analysis it is shown that the leading term in these expansions is suitably close to the uniquely determined exact solution. The pulses considered can have multiple components, some of which reflect off fixed non characteristic boundaries in a spectrally stable way (in the sense of Kreiss), and some of which decay exponentially away from the boundary. The results in this paper provide a generalization to the work of Coulombel and Williams, as the boundary frequency is considered not only in the hyperbolic region, but also in the mixed and elliptic regions. Furthermore the boundary data considered in this paper is more general than the boundary data considered in the work of Coulombel and Williams. In fact, it is shown in this paper that "theta-decay" inheritance of the boundary data to the solution is in some cases not even possible.
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  • In Copyright
Advisor
  • Marzuola, Jeremy
  • Jones, Christopher K. R. T.
  • Williams, Mark
  • Camassa, Roberto
  • Taylor, Michael Eugene
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2015
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Place of publication
  • Chapel Hill, NC
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