Kevin Zumbrun in Paris

Talks

Shock waves and beyond

June 23-26
Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05
Organization committee: Benjamin Texier, Kevin Zumbrun
Scientific committee: Peter Howard, Pascal Noble, Jeffrey Rauch, Benjamin Texier, Kevin Zumbrun
Speakers: Sylvie Benzoni, Lydia Bieri, Alberto Bressan, Laura Caravenna, Gianluca Crippa, Anne-Laure Dalibard, Heinrich Freistühler, Pierre Germain, David Lannes, Gregory Lyng, Guy Métivier, Roberto Natalini, Toan Nguyen, Luis-Miguel Rodrigues, Frédéric Rousset, Denis Serre, Franck Sueur, Laszlo Székelyhidi Jr., Julien Vovelle, Mark Williams



Slides of previous talks

Click here to download the slides of the talk Nonlinear damping estimates and stability of large-amplitude periodic wave trains (Séminaire Analyse Numérique et Equations aux Dérivées Partielles (PDE Seminar), Université Paris-Sud)

Click here to download the slides of the talk Corrugation instability and bifurcation of slow viscous MHD shocks in a duct (Séminaire de Physique Mathématique - EDP, Université de Bordeaux 1)




Course: Stability of viscous shock waves and beyond

Kevin Zumbrun (Indiana University), 2014 Research Chair of the FSMP, gave a 32-hour course during his stay at the IMJ-PRG. His course was entitled: "Stability of viscous shock waves and beyond".  

All lectures took place at the Institut Henri Poincaré (11 rue Pierre et Marie Curie Paris, 5ème) from 2pm to 4pm on:

- 03/02/2015 : Room 314 LECTURE CANCELLED

- 05/02/2015 : Room 314
- 10/02/2015 : Room 314
- 12/02/2015 : Room 314
- 17/02/2015 : Room 314
- 19/02/2015 : Room 314
- 24/02/2015 : Room 314
- 26/02/2015 : Room 201
- 03/03/2015 : Room 314

- 05/03/2015 : Room 314 LECTURE CANCELLED

- 10/03/2015 : Room 314

- 11/03/2015 : Room 314 LECTURE CANCELLED

- 12/03/2015 : Room 314
- 17/03/2015 : Room 01
- 24/03/2015 : Room 314
- 26/03/2015 : Room 314
- 31/03/2015 : Room 201

Keywords: Stability and bifurcation of viscous shock waves, numerical Evans function evaluation and spectra of differential operators, Evans vs. Lopatinski determinants and relations between viscous and inviscid stability, modulation of spatially periodic waves. 

Click here to read the course's description.  



Lectures & Guests

- 19/02/2015 : Blake Barker

- 24/02/2015 : Blake Barker

- 26/02/2015 : Blake Barker

- 03/03/2015 : Benjamin Texier and Blake Barker

- 10/03/2015 : Guy Métivier

- *11/03/2015* : Guy Métivier

- 12/03/2015 : Luis-Miguel Rodrigues

- 17/03/2015 : Luis-Miguel Rodrigues

- 24/03/2015 : Björn Sandstede

- 26/03/2015 : Björn Sandstede


Videos and lecture notes

Lecture #1 - 05/02/2015
First hour
Second hour



Lecture #2 - 10/02/2015
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Second hour

 

Lecture #3 - 12/02/2015
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Second hour




Lecture #4 - 17/02/2015
First hour
Second hour




Lecture #5 - 19/02/2015

First hour
Second hour : Stability of viscous shocks in isentropic gas dynamics and Existence and Stability of Viscous Shock Profiles for Isentropic MHD with Infinite Electrical Resistivity



Lecture #6 - 24/02/2015
First hour
Second hour 




Lecture #7 - 26/02/2015
First hour
Second hour 


Lecture #8 - 03/03/2015
First hour
Second hour




Lecture #9 - 10/03/2015
Lecture notes




Lecture #10 - 12/03/2015

Lecture notes


Lecture #11 - 17/03/2015
Lecture notes


Lecture #12 - 24/03/2015
Lectures notes




Lecture #13 - 26/03/2015
 


Last lecture - 31/03/2015
First hour
Second hour




Subdirectories

Numerical proof

Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow, by Blake Barker


Theoretical Evans analyses

Spectral stability of small-amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems, by Jeffrey Humpherys and Kevin Zumbrun

Stability of noncharacteristic boundary layers in the standing-shock limit, by Kevin Zumbrun

Stability of detonation profiles in the ZND limit, by Kevin Zumbrun 

Numerical Evans analyses

An efficient shooting algorithm for Evans function calculations in large systems, by Jeffrey Humpherys and Kevin Zumbrun

Stability of Isentropic Navier-Stokes Shocks in the High-Mach Number Limit, by Jeffrey Humpherys, Olivier Lafitte and Kevin Zumbrun

Existence and stability of viscous shock profiles for 2-D isentropic MHD with infinite electrical resistivity, by Blake Barker, Olivier Lafitte, and Kevin Zumbrun 

Spectral stability of ideal-gas shock layers, by Jeffrey Humpherys, Gregory Lyng and Kevin Zumbrun

One-dimensial stability of parallel shock layers in isentropic magnetohydrodynamics, by Blake Barker, Jeffrey Humpherys and Kevin Zumbrun 

Viscous hyperstabilization of detonation waves in one space dimension, by Blake Barker, Jeffrey Humpherys, Gregory Lyng, and Kevin Zumbrun

A numerical stability investigation of strong ZND detonations for Majda's model, by Blake Barker and Kevin Zumbrun

Existence and stability of viscoelastic shock profiles, by Blake Barker, Marta Lewicka and Kevin Zumbrun

Surveys

Stability of large-amplitude shock waves of compressible Navier-Stokes equations, by Kevin Zumbrun


Modulation of periodic wave-trains

Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability, by Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues and Kevin Zumbrun

Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation, by Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues and Kevin Zumbrun

Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations, by Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues and Kevin Zumbrun 

Stability of viscous St. Venant roll-waves: from onset to infinite-froude number limit, by Blake Barker, Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues and Kevin Zumbrun 

Asymptotic stability and modulation of periodic wavetrains, by L. Miguel Rodrigues

Whitham's Modulation Equations and Stability of Periodic Wave Solutions of the Korteweg-de-Vries-Kuramoto-Sivashinsky Equation, by Pascal Noble and L. Miguel Rodrigues  

Nonlinear damping estimates

Periodic-coefficient damping estimates, and stability of large-amplitude roll waves in inclined thin film flow, par L. Miguel Rodrigues et Kevin Zumbrun