Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems

Mark Williams

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arXiv · 2207.14173

Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems

Mark Williams

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Abstract

We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions $n>1$. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The justification applies to $N\times N$ systems with $N$ interacting pulses which depend on phases that may be nonlinear. The \emph{coherence} assumption made in a number of earlier works is dropped. We consider problems in which incoming pulses are generated from pulse boundary data as well as problems in which a single outgoing pulse reflects off a possibly curved boundary to produce a number of incoming pulses. Although we focus here on boundary problems, it is clear that similar results hold by similar methods for the Cauchy problem for $N\times N$ systems in free space.

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Mark Williams. 2022-07-28. Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems. https://arxiv.org/abs/2207.14173

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