# Williams, Mark

Professor

Phillips Hall 380

WILLIAMS@email.unc.edu

Website

## Research Interests

Partial differential equations

## Professional Background

B.S., Knox College 1977; Ph.D. MIT 1981

## Research Synopsis

It is generally impossible to solve a partial differential equation explicitly. One can often prove existence and uniqueness results using techniques from functional analysis, but these results do not provide detailed qualitative information about solutions. My research is largely concerned with developing methods for obtaining qualitative information about solutions.

## Representative Publications

*Geometric Optics for Surface Waves in Nonlinear Elasticity*

J.-F. Coulombel and M. Williams,

Memoirs of the American Mathematical Society, 263, 1271, 2020

*The Mach Stem Equation and Amplification in Strongly Nonlinear Geometric*

J.-F. Coulombel and M. Williams,

American Journal of Mathematics, 139, 967-1046, 2017

*Multidimensional Viscous Shocks I: Degenerate Symmetrizers and Long Time Stability*

O. Gues, G. Metivier, M. Williams, K. Zumbrun,

Journal of the American Mathematical Society, 18, 61-120, 2005