28 citations · 49 across the 17 of their papers we have counts for
16 papers · 1 filter
Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems
Mark Williams
We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions . The pulses arise as solutions to variable coeffic…
Hyperbolic boundary problems with large oscillatory coefficients: multiple amplification
Mark Williams
We study weakly stable hyperbolic boundary problems with highly oscillatory coefficients that are large, , compared to the small wavelength $\eps$ of oscillations. Such probl…
On the Mach stem configuration with shallow angle
Jean-François Coulombel, Mark Williams
The aim of this article is to explain why similar weak stability criteria appear in both the construction of steady Mach stem configurations bifurcating from a reference planar sho…
Geometric optics for Rayleigh wavetrains in d-dimensional nonlinear elasticity
Aric Wheeler, Mark Williams
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been don…
Geometric optics for surface waves in nonlinear elasticity
Jean-Francois Coulombel, Mark Williams
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. We consider surface waves (or more precisely, Rayleigh wa…
The Mach stem equation and amplification in strongly nonlinear geometric optics
Jean-Francois Coulombel, Mark Williams
We study highly oscillating solutions to a class of weakly well-posed hyperbolic initial boundary value problems. Weak well-posedness is associated with an amplification phenomenon…