Stabilité de couches limites multi-dimensionnelles

Guy Métivier[1]; Kevin Zumbrun[2]

  • [1] MAB Université de Bordeaux I, 33405 Talence Cedex France
  • [2] Indiana University, Bloomington, IN 47405 USA

Séminaire Équations aux dérivées partielles (2002-2003)

  • Volume: 2002-2003, page 1-15

How to cite

top

Métivier, Guy, and Zumbrun, Kevin. "Stabilité de couches limites multi-dimensionnelles." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-15. <http://eudml.org/doc/11062>.

@article{Métivier2002-2003,
affiliation = {MAB Université de Bordeaux I, 33405 Talence Cedex France; Indiana University, Bloomington, IN 47405 USA},
author = {Métivier, Guy, Zumbrun, Kevin},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {viscous boundary layers; stability of multidimensional shocks; Evans function; homogeneous Dirichlet condition; linear stability; nonlinear stability},
language = {fre},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Stabilité de couches limites multi-dimensionnelles},
url = {http://eudml.org/doc/11062},
volume = {2002-2003},
year = {2002-2003},
}

TY - JOUR
AU - Métivier, Guy
AU - Zumbrun, Kevin
TI - Stabilité de couches limites multi-dimensionnelles
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 15
LA - fre
KW - viscous boundary layers; stability of multidimensional shocks; Evans function; homogeneous Dirichlet condition; linear stability; nonlinear stability
UR - http://eudml.org/doc/11062
ER -

References

top
  1. J. Alexander-R. Gardner-C.K.R.T. Jones, A topological invariant arising in the analysis of traveling waves. J. Reine Angew. Math. 410 (1990) 167–212. Zbl0705.35070MR1068805
  2. A. Azevedo-D. Marchesin-B. Plohr-K. Zumbrun, Nonuniqueness of solutions of Riemann problems. Z. Angew. Math. Phys. 47 (1996), 977–998. Zbl0880.35068MR1424039
  3. C.Bardos-D.Brezis-H.Brezis, Perturbations singulières et prolongement maximaux d’opérateurs positifs, Arch.Rational Mech. Anal., 53 (1973), 69–100. Zbl0281.47028
  4. C.Bardos-J.Rauch Maximal positive boundary value problems as limits of singular perturbation problems, Trans. Amer.Math.Soc., 270 (1982), 377–408. Zbl0485.35010MR645322
  5. J. Chazarain-A. Piriou, Introduction to the theory of linear partial differential equations, Translated from the French. Studies in Mathematics and its Applications, 14. North-Holland Publishing Co., Amsterdam-New York, 1982. xiv+559 pp. ISBN : 0-444-86452-0. Zbl0487.35002MR678605
  6. J.W. Evans, Nerve axon equations : I. Linear approximations. Ind. Univ. Math. J. 21 (1972) 877–885. Zbl0235.92002MR292531
  7. J.W. Evans, Nerve axon equations : II. Stability at rest. Ind. Univ. Math. J. 22 (1972) 75–90. Zbl0236.92010MR323372
  8. J.W. Evans, Nerve axon equations : III. Stability of the nerve impulse. Ind. Univ. Math. J. 22 (1972) 577–593. Zbl0245.92004MR393890
  9. J.W. Evans, Nerve axon equations : IV. The stable and the unstable impulse. Ind. Univ. Math. J. 24 (1975) 1169–1190. Zbl0317.92006MR393891
  10. R. Gardner-K. Zumbrun, The Gap Lemma and geometric criteria for instability of viscous shock profiles. Comm. Pure Appl. Math. 51 (1998), 797–855. Zbl0933.35136MR1617251
  11. M. Gisclon-D. Serre, Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov. RAIRO Modél. Math. Anal. Numér. 31 (1997), 359–380. Zbl0873.65087MR1451347
  12. E. Grenier On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (2000), no. 9, 1067–1091. Zbl1048.35081MR1761409
  13. E. Grenier-O. Guès, Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems. J. Differential Equations 143 (1998), 110–146. Zbl0896.35078MR1604888
  14. E. Grenier-F. Rousset, Stability of one-dimensional boundary layers by using Green’s functions. Comm. Pure Appl. Math. 54 (2001), 1343–1385. Zbl1026.35015
  15. O.Guès, Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann.Inst.Fourier, 45 (1995),973–1006. Zbl0831.34023MR1359836
  16. O.Guès-G.Métivier-M.Williams-K.Zumbrun Multidimensional viscous shocks I : Degenerate symmetrizers and long time stability preprint Zbl1058.35163MR2114817
  17. O.Guès-G.Métivier-M.Williams-K.Zumbrun Multidimensional viscous shocks II : The small viscosity limit preprint. Zbl1073.35162MR2012648
  18. D. Hoff-K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ. Math. J. 44 (1995), 603–676. Zbl0842.35076MR1355414
  19. C.K.R.T. Jones, Stability of the travelling wave solution of the FitzHugh–Nagumo system. Trans. Amer. Math. Soc. 286 (1984), 431–469. Zbl0567.35044MR760971
  20. T. Kapitula, On the stability of travelling waves in weighted L spaces. J. Diff. Eqs. 112 (1994), 179–215. Zbl0803.35067MR1287557
  21. H.O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970) 277-298. Zbl0193.06902MR437941
  22. J.L.Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lectures Notes in Math., 323, Sringer Verlag, 1973. Zbl0268.49001MR600331
  23. A. Majda, The stability of multi-dimensional shock fronts – a new problem for linear hyperbolic equations. Mem. Amer. Math. Soc. 275 (1983). Zbl0506.76075MR683422
  24. G. Métivier, Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d’espace. Trans. Amer. Math. Soc. 296 (1986) 431–479. Zbl0619.35075
  25. G. Métivier, Stability of multidimensional shocks. Advances in the theory of shock waves, 25–103, Progr. Nonlinear Differential Equations Appl., 47, Birkhäuser Boston, Boston, MA, 2001. Zbl1017.35075MR1842775
  26. G.Métivier. The Block Structure Condition for Symmetric Hyperbolic Problems, Bull. London Math.Soc., 32 (2000), 689–702 Zbl1073.35525MR1781581
  27. G.Métivier-K.Zumbrun, Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems, preprint. Zbl1074.35066
  28. A.Mokrane Problèmes mixtes hyperboliques non linéaires, Thesis, Université de Rennes 1, 1987. 
  29. R. L. Pego-M.I. Weinstein, Eigenvalues, and instabilities of solitary waves. Philos. Trans. Roy. Soc. London Ser. A 340 (1992), 47–94. Zbl0776.35065MR1177566
  30. J. Rauch-F. Massey, Differentiability of solutions to hyperbolic initial boundary value problems. Trans. Amer. Math. Soc. 189 (1974) 303-318. Zbl0282.35014MR340832
  31. F. Rousset, Inviscid boundary conditions and stability of viscous boundary layers. Asymptotic. Anal. 26 (2001), no. 3-4, 285–306. Zbl0977.35081MR1844545
  32. D. Serre, Sur la stabilité des couches limites de viscosité. Ann. Inst. Fourier (Grenoble) 51 (2001), 109–130. Zbl0963.35009MR1821071
  33. M.Taylor. Partial Differential EquationsIII, Applied Mathematical Sciences 117, Springer, 1996. Zbl0869.35004MR1395147
  34. K. Zumbrun-D.Serre, Viscous and inviscid stability of multidimensional planar shock fronts. Indiana Univ. Math. J. 48 (1999), 937–992. Zbl0944.76027MR1736972
  35. K. Zumbrun-P. Howard, Pointwise semigroup methods and stability of viscous shock waves. Indiana Mathematics Journal V47 (1998), 741–871. Zbl0928.35018MR1665788
  36. K. Zumbrun, Multidimensional stability of planar viscous shock waves. Advances in the theory of shock waves, 307–516, Progr. Nonlinear Differential Equations Appl., 47, Birkhäuser Boston, Boston, MA, 2001. Zbl0989.35089MR1842778

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.