Mark Williams

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All published works

Action	Title	Year	Authors
+	Transport of Nonlinear Oscillations Along Rays that Graze a Convex Obstacle to any Order	2025	Jian Wang Mark Williams
+ PDF Chat	Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems	2024	Mark Williams
+	Transport of nonlinear oscillations along rays that graze a convex obstacle to any order	2023	Jian Wang Mark Williams
+	Hyperbolic boundary problems with large oscillatory coefficients: Multiple amplification	2020	Mark Williams
+	Weakly stable hyperbolic boundary problems with large oscillatory coefficients: Simple cascades	2020	Mark Williams
+	Geometric Optics for Surface Waves in Nonlinear Elasticity	2020	Jean-François Coulombel Mark Williams
+ PDF Chat	On the Mach stem configuration with shallow angle	2020	Jean-François Coulombel Mark Williams
+	Hyperbolic boundary problems with large oscillatory coefficients: multiple amplification	2019	Mark Williams
+	Geometric optics for Rayleigh wavetrains in d-dimensional nonlinear elasticity	2018	Aric Wheeler Mark Williams
+	Geometric Optics for Rayleigh Wavetrains in d-Dimensional	2018	Aric Wheeler Mark Williams
+	The Mach stem equation and amplification in strongly nonlinear geometric optics	2017	Jean-François Coulombel Mark Williams
+	Geometric Optics for Rayleigh Pulses in Nonlinear Elasticity	2017	Mark Williams
+	Block-Diagonalization of ODEs in the Semiclassical Limit and $C^\omega$ versus $C^\infty$ Stationary Phase	2016	Olivier Lafitte Mark Williams Kevin Zumbrun
+	Block-diagonalization of ODEs in the semiclassical limit and $C^\omega$ vs. $C^\infty$ stationary phase	2015	Olivier Lafitte Mark Williams Kevin Zumbrun
+	Block-diagonalization of ODEs in the semiclassical limit and $C^ω$ vs. $C^\infty$ stationary phase	2015	Olivier Lafitte Mark Williams Kevin Zumbrun
+ PDF Chat	Amplification of pulses in nonlinear geometric optics	2014	Jean-François Coulombel Mark Williams
+ PDF Chat	Semilinear geometric optics with boundary amplification	2014	Jean-François Coulombel Olivier Guès Mark Williams
+ PDF Chat	Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions	2014	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+ PDF Chat	Singular pseudodifferential calculus for wavetrains and pulses	2014	Jean-François Coulombel Olivier Guès Mark Williams
+	High-frequency stability of multidimensional ZND detonations	2013	Olivier Lafitte Mark Williams Kevin Zumbrun
+	Nonlinear geometric optics for reflecting uniformly stable pulses	2013	Jean-François Coulombel Mark Williams
+ PDF Chat	The inviscid limit and stability of characteristic boundary layers for the compressible Navier-Stokes equations with Navier-friction boundary conditions	2012	Ya-Guang Wang Mark Williams
+ PDF Chat	The Erpenbeck High Frequency Instability Theorem for Zeldovitch–von Neumann–Döring Detonations	2011	Olivier Lafitte Mark Williams Kevin Zumbrun
+ PDF Chat	Resonant Leading Order Geometric Optics Expansions for Quasilinear Hyperbolic Fixed and Free Boundary Problems	2011	Jean-François Coulombel Olivier Guès Mark Williams
+	Advances in Sensitivity Analysis Capabilities with SCALE 6.0 and 6.1	2010	Bradley T. Rearden L.M. Petrie Mark Williams
+ PDF Chat	Singularly perturbed ODEs and profiles for stationary symmetric Euler and Navier-Stokes shocks	2010	Erik Endres Helge Kristian Jenssen Mark Williams
+ PDF Chat	Existence and Stability of Noncharacteristic Boundary Layers for the Compressible Navier–Stokes and Viscous MHD Equations	2009	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain	2008	Erik Endres Helge Kristian Jenssen Mark Williams
+ PDF Chat	Nonclassical multidimensional viscous and inviscid shocks	2008	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Viscous boundary value problems for symmetric systems with variable multiplicities	2007	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Hyperbolic Systems of Balance Laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003	2007	Alberto Bressan Denis Serre Mark Williams Kevin Zumbrun Pierangelo Marcati
+ PDF Chat	Uniform Stability Estimates for Constant-Coefficient Symmetric Hyperbolic Boundary Value Problems	2007	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Stability of Multidimensional Viscous Shocks	2007	Mark Williams
+	Hyperbolic Systems of Balance Laws	2007	Alberto Bressan Denis Serre Mark Williams Kevin Zumbrun
+	Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities	2006	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+ PDF Chat	Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion	2005	Helge Kristian Jenssen Gregory D. Lyng Mark Williams
+	Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems	2005	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability	2004	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+ PDF Chat	Boundary layer and long time stability for multi-D viscous shocks	2004	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Multidimensional viscous shocks II: The small viscosity limit	2003	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun
+	Singular Pseudodifferential Operators, Symmetrizers, and Oscillatory Multidimensional Shocks	2002	Mark Williams
+ PDF Chat	Curved shocks as various limits: a boundary problem approach	2002	Olivier Guès Mark Williams
+	Highly oscillatory multidimensional shocks	1999	Mark Williams
+	Nonlinear Geometric Optics for Reflecting and Glancing Oscillations	1997	Mark Williams
+	Nonlinear geomettic optics for hyperbolic boundary problems	1996	Mark Williams
+	Natural convection of a radiating fluid in a square enclosure with perfectly conducting end walls	1994	Adnan Yücel S. Acharya Mark Williams
+	Interaction of Singularities and Propagation into Shadow Regions in Semilinear Boundary Problems	1991	Mark Williams
+	Interactions involving gliding rays in boundary problems for semilinear wave equations	1989	Mark Williams
+ PDF Chat	Spreading of singularities at the boundary in semilinear hyperbolic mixed problems. II. Crossing and self-spreading	1989	Mark Williams
+	Spreading of Singularities at the Boundary in Semilinear Hyperbolic Mixed Problems II: Crossing and Self-Spreading	1989	Mark Williams
+	Spreading of singularities at the boundary in semilinear hyperbolic mixed problems I: Microlocal Hs,s′ regularity	1988	Mark Williams
+	Singularities of Solutions to Semilinear Boundary Value Problems	1987	F. Anderson David Mark Williams
+	Combined radiation and conduction in axisymmetric enclosures by the discrete ordinates method	1986	Adnan Yücel Mark Williams
+ PDF Chat	On extending solutions to wave equations across glancing boundaries	1986	Mark Williams
+ PDF Chat	Propagation of singularities of solutions to semilinear boundary value problems	1986	F. Anderson David Mark Williams
+	On extending solutions to Dirichlet problems across the boundary as solutions	1985	Mark Williams
+	Wa vefront sets of extensions of solutions to diffractive boundary problems.	1983	Mark Williams
+ PDF Chat	Development of Depletion Perturbation Theory for Coupled Neutron/Nuclide Fields	1979	Mark Williams

Common Coauthors

Coauthor	Papers Together
Kevin Zumbrun	17
Olivier Guès	14
Guy Métivier	7
Jean-François Coulombel	5
Olivier Lafitte	5
Guy Métivier	3
Helge Kristian Jenssen	3
Jean-François Coulombel	3
Aric Wheeler	2
Denis Serre	2
Alberto Bressan	2
F. Anderson David	2
Adnan Yücel	2
Jian Wang	2
Erik Endres	2
Ya-Guang Wang	1
L.M. Petrie	1
Bradley T. Rearden	1
Pierangelo Marcati	1
Gregory D. Lyng	1
S. Acharya	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Initial boundary value problems for hyperbolic systems	1970	Heinz‐Otto Kreiss	26
+	Introduction to the Theory of Linear Partial Differential Equations	1982	Jacques Chazarain Alain Piriou	21
+	The stability of multidimensional shock fronts	1983	Andrew J. Majda	16
+ PDF Chat	The Block Structure Condition for Symmetric Hyperbolic Systems	2000	Guy Métivier	15
+	The existence of multidimensional shock fronts	1983	Andrew J. Majda	12
+	Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems	2005	Guy Métivier Kevin Zumbrun	12
+ PDF Chat	Navier–Stokes regularization of multidimensional Euler shocks	2006	C GUES Guy Métivier M. C. S. Williams Kevin Zumbrun	11
+	Singularities of boundary value problems. I	1978	Richard Melrose Johannes Sjöstrand	10
+	Boundary Layers for Viscous Perturbations of Noncharacteristic Quasilinear Hyperbolic Problems	1998	Emmanuel Grenier Olivier Guès	10
+	Singular Pseudodifferential Operators, Symmetrizers, and Oscillatory Multidimensional Shocks	2002	Mark Williams	10
+ PDF Chat	Existence and Stability of Multidimensional Shock Fronts in the Vanishing Viscosity Limit	2004	Olivier Guès Guy Métivier Mark V. Williams Kevin Zumbrun	10
+ PDF Chat	Viscous and inviscid stability of multidimensional planar shock fronts	1999	Olivier Lafitte	9
+ PDF Chat	Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems	2010	Jean-François Coulombel Olivier Guès	9
+	Asymptotic solutions of oscillatory initial value problems	1957	Peter D. Lax	9
+	Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability	2004	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun	9
+	The gap lemma and geometric criteria for instability of viscous shock profiles	1998	Robert A. Gardner Kevin Zumbrun	9
+	Hyperbolic boundary value problems for symmetric systems with variable multiplicities	2004	Guy Métivier Kevin Zumbrun	9
+	Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension	1982	Jeffrey Rauch Michael C. Reed	8
+	Multi-dimensional hyperbolic partial differential equations	2006	Sylvie Benzoni-Gavage Denis Serre	8
+ PDF Chat	Curved shocks as various limits: a boundary problem approach	2002	Olivier Guès Mark Williams	8
+	Multidimensional Stability of Planar Viscous Shock Waves	2001	Kevin Zumbrun	8
+	Multidimensional viscous shocks II: The small viscosity limit	2003	Olivier Guès Guy Métivier Mark Williams Kevin Zumbrun	8
+ PDF Chat	Semilinear geometric optics with boundary amplification	2014	Jean-François Coulombel Olivier Guès Mark Williams	7
+ PDF Chat	Pointwise semigroup methods and stability of viscous shock waves	1998	Kevin Zumbrun Peter Howard	7
+ PDF Chat	Resonant Leading Order Geometric Optics Expansions for Quasilinear Hyperbolic Fixed and Free Boundary Problems	2011	Jean-François Coulombel Olivier Guès Mark Williams	7
+	Nonlinear geomettic optics for hyperbolic boundary problems	1996	Mark Williams	7
+	Viscous limits for piecewise smooth solutions to systems of conservation laws	1992	Jonathan Goodman Zhouping Xin	7
+	Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems	2004	Guy Métivier Kevin Zumbrun	7
+	Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves	1993	J. L. Joly Guy Métivier J. Rauch	7
+ PDF Chat	Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations	2005	Kevin Zumbrun Helge Kristian Jenssen Gregory D. Lyng	7
+	Highly oscillatory multidimensional shocks	1999	Mark Williams	7
+ PDF Chat	Boundary layers and glancing blow-up in nonlinear geometric optics	2000	M. C. S. Williams	6
+ PDF Chat	Régularité microlocale pour des problèmes aux limites non linéaires	1986	Monique Sablé-Tougeron	6
+ PDF Chat	Singular pseudodifferential calculus for wavetrains and pulses	2014	Jean-François Coulombel Olivier Guès Mark Williams	6
+	An Evans function approach to spectral stability of small-amplitude shock profiles	2004	Ramón G. Plaza Kevin Zumbrun	6
+	Generic types and transitions in hyperbolic initial–boundary-value problems	2002	Sylvie Benzoni-Gavage Frédéric Rousset Denis Serre Kevin Zumbrun	6
+	Well-posedness of hyperbolic initial boundary value problems	2005	Jean-François Coulombel	6
+	Singularities of boundary value problems. II	1982	Richard Melrose Johannes Sjöstrand	6
+	Spectral Stability of Small Shock Waves	2002	Heinrich Freistühler Peter Szmolyan	6
+	Stability of Multidimensional Shocks	2001	Guy Métivier	6
+	Advances in the Theory of Shock Waves	2001	Tai-Ping Liu Guy Métivier Joel Smoller Blake Temple Wen‐An Yong Kevin Zumbrun	5
+	<i>Theory of Ordinary Differential Equations</i>	1956	Earl A. Coddington Norman Levinson T. Teichmann	5
+	Singularities of Solutions to Semilinear Boundary Value Problems	1987	F. Anderson David Mark Williams	5
+ PDF Chat	On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws	1988	Shuichi Kawashima Yasushi Shizuta	5
+	The Mach stem equation and amplification in strongly nonlinear geometric optics	2017	Jean-François Coulombel Mark Williams	5
+ PDF Chat	Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation	1985	Yasushi Shizuta Shuichi Kawashima	5
+	Stability and Asymptotic Behavior of Differential Equations.	1968	F. S. Van Vleck W. A. Coppel	5
+ PDF Chat	Diffractive Nonlinear Geometric Optics for Short Pulses	2003	Deborah Alterman Jeffrey Rauch	5
+	Stability of one‐dimensional boundary layers by using Green's functions	2001	Emmanuel Grenier Frédéric Rousset	5
+	Zero-Dissipation Limit of Solutions with Shocks for Systems of Hyperbolic Conservation Laws	1999	Shih‐Hsien Yu	5