Faculty

Institution

Unit

Venue

Mark Williams

Professor

University of North Carolina at Chapel Hill

Affiliations

College of Arts and Sciences

Mathematics

Mark Williams is currently serving as a College Of Arts And Sciences Professor at University of North Carolina At Chapel Hill.

Honors

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Experiences

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Education

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Mark Williams

University of North Carolina at Chapel Hill

Professor

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applied mathematics mathematics boundary value problems partial differential equations fluid dynamics dynamical systems nonlinear science differential equations numerical analysis hyperbolic equations fluid mechanics nonlinear phenomena nonlinear dynamics numerical method for partial differential equation applied physics mechanical engineering mathematical physics numerical simulations nonlinear hyperbolic problem nonlinear geometric optics geometrical optics detonation phenomenon differential geometry computational fluid dynamics shock waves spectral theory nonlinear analysis mathematical optimization numerical mathematics boundary layers hydrodynamic stability free boundary problems singularly perturbed problem hyperbolic conservation laws wave propagation geometric singular perturbation theory unsteady flows compressible flows discrete dynamical systems nonlinear wave propagation bifurcation theory long time stability oscillatory multidimensional shocks hyperbolic systems balance laws navier-stokes shocks rational mechanic friction geometric topology fluid flow social science research fourier analysis compression (physics) global analysis shock compression nonlinear functional analysis nonlinear equations optical amplifier finite fields nonlinear signal processing stochastic calculus dynamical analysis chaotic mixing symbolic dynamics microlocal analysis source apportionment degenerate symmetrizers small viscosity limit viscous mhd equations compressible navier-stokes noncharacteristic boundary layers compressible navier-stokes equations characteristic boundary layers navier-friction boundary conditions inviscid limit multi-d viscous shocks

Notable Scholarly Works

Notable Federal Grants

Collaborators

Reflection of Conormal Pulse Solutions to Large Variable-Coefficient Semilinear Hyperbolic Systems. Journal of Differential Equations (2024)

Mark Williams

fluid dynamicsnonlinear systemsengineeringapplied mathematicshyperbolic conservation lawsconormal pulse solutionspartial differential equationsnonlinear phenomenadynamical systemsnonlinear dynamicsnonlinear sciencewave propagationhyperbolic equationsnumerical method for partial differential equationdifferential equationsnumerical simulationsmechanical engineeringnonlinear hyperbolic problem

Geometric Optics for Surface Waves in Nonlinear Elasticity. Memoirs of the American Mathematical Society (2020)

Jean-François CoulombelMark Williams

nonlinear wave propagationapplied mathematicssurface wavesoptical propertiesgeometrical opticsgeometric relativitygeometric opticsapplied physicsnonlinear sciencephysicsnonlinear elasticity

Hyperbolic Boundary Problems With Large Oscillatory Coefficients: Multiple Amplification. Journal of Differential Equations (2020)

Mark Williams

ordinary differential equationsdifferential equationsnumerical simulationslarge oscillatory coefficientsnonlinear hyperbolic problemmultiple amplificationoscillation theoryhyperbolic boundary problemsfluid mechanicscomputational fluid dynamicsnonlinear dynamicsnumerical method for partial differential equationnonlinear sciencehyperbolic equationsapplied mathematicspartial differential equationsdynamical systemsperturbation methodsboundary value problemsjournalism

On the Mach Stem Configuration With Shallow Angle. Indiana University Mathematics Journal (2020)

Jean-François CoulombelMark Williams

shallow angleapplied mathematicsmach stem configurationmathematicsmechanical engineering

Weakly Stable Hyperbolic Boundary Problems With Large Oscillatory Coefficients: Simple Cascades. Journal of Hyperbolic Differential Equations (2020)

Mark Williams

oscillation theorysimple cascadeshyperbolic conservation lawspartial differential equationsdynamical systemsnonlinear sciencephysicshyperbolic equationsordinary differential equationsdifferential equationsboundary value problemslarge oscillatory coefficientsnonlinear hyperbolic problem

Geometric Optics for Rayleigh Wavetrains in D-Dimensional Nonlinear Elasticity. arXiv (Cornell University) (2018)

Aric WheelerMark Williams

d-dimensional nonlinear elasticityrayleigh wavetrainsgeometric opticsphysicsnonlinear elasticity

Geometric Optics for Rayleigh Pulses in Nonlinear Elasticity. Springer INdAM series (2017)

Mark Williams

rayleigh pulsesnonlinear elasticityphysicsgeometric optics

The Framework of a Novel Approach for the Analysis of Human Movement for Clinical Purposes. Open Journal of Social Sciences (2017)

Mark E. WilliamsJohn C. C. Williams

social science researchmotion analysisclinical purposesmovement analysisopen researchsocial sciencesapplied social sciencephysiologypublic healthbiomedical analysisopen sciencegait analysishuman movement

The Mach Stem Equation and Amplification in Strongly Nonlinear Geometric Optics. American Journal of Mathematics (2017)

Jean-François CoulombelMark Williams

applied mathematicsmach stem equationnonlinear sciencemathematicsnonlinear equationsnonlinear geometric optics

Block-Diagonalization of Odes in the Semiclassical Limit and $C^\Omega$ Versus $C^\Infty$ Stationary Phase. SIAM Journal on Mathematical Analysis (2016)

Olivier LafitteMark WilliamsKevin Zumbrun

semiclassical limitapplied mathematicsmathematicsstationary phasemathematical analysis

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Mark Williams

Professor

University of North Carolina at Chapel Hill

Affiliations

College of Arts and Sciences

Mathematics

Mark Williams is currently serving as a College Of Arts And Sciences Professor at University of North Carolina At Chapel Hill.

Honors

Create free account to unlock more features

Experiences

Create free account to unlock more features

Education

Create free account to unlock more features

Mark Williams

University of North Carolina at Chapel Hill

Professor

You can click a keyword to filter the displayed items

Notable Scholarly Works

Notable Federal Grants

Collaborators

Reflection of Conormal Pulse Solutions to Large Variable-Coefficient Semilinear Hyperbolic Systems. Journal of Differential Equations (2024)

Mark Williams

Geometric Optics for Surface Waves in Nonlinear Elasticity. Memoirs of the American Mathematical Society (2020)

Jean-François CoulombelMark Williams

nonlinear wave propagationapplied mathematicssurface wavesoptical propertiesgeometrical opticsgeometric relativitygeometric opticsapplied physicsnonlinear sciencephysicsnonlinear elasticity

Hyperbolic Boundary Problems With Large Oscillatory Coefficients: Multiple Amplification. Journal of Differential Equations (2020)

Mark Williams

On the Mach Stem Configuration With Shallow Angle. Indiana University Mathematics Journal (2020)

Jean-François CoulombelMark Williams

shallow angleapplied mathematicsmach stem configurationmathematicsmechanical engineering

Weakly Stable Hyperbolic Boundary Problems With Large Oscillatory Coefficients: Simple Cascades. Journal of Hyperbolic Differential Equations (2020)

Mark Williams

Geometric Optics for Rayleigh Wavetrains in D-Dimensional Nonlinear Elasticity. arXiv (Cornell University) (2018)

Aric WheelerMark Williams

d-dimensional nonlinear elasticityrayleigh wavetrainsgeometric opticsphysicsnonlinear elasticity

Geometric Optics for Rayleigh Pulses in Nonlinear Elasticity. Springer INdAM series (2017)

Mark Williams

rayleigh pulsesnonlinear elasticityphysicsgeometric optics

The Framework of a Novel Approach for the Analysis of Human Movement for Clinical Purposes. Open Journal of Social Sciences (2017)

Mark E. WilliamsJohn C. C. Williams

The Mach Stem Equation and Amplification in Strongly Nonlinear Geometric Optics. American Journal of Mathematics (2017)

Jean-François CoulombelMark Williams

applied mathematicsmach stem equationnonlinear sciencemathematicsnonlinear equationsnonlinear geometric optics

Block-Diagonalization of Odes in the Semiclassical Limit and $C^\Omega$ Versus $C^\Infty$ Stationary Phase. SIAM Journal on Mathematical Analysis (2016)

Olivier LafitteMark WilliamsKevin Zumbrun

semiclassical limitapplied mathematicsmathematicsstationary phasemathematical analysis

1
2
3
4
5
10 / page

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Institution

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