@article{JEDP_2006____A1_0, author = {M\'etivier, Guy}, title = {Lecture notes : {Stability} of {Noncharacteristic} {Viscous} {Boundary} {Layers}}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {1}, pages = {1--82}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2006}, doi = {10.5802/jedp.28}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.28/} }
TY - JOUR AU - Métivier, Guy TI - Lecture notes : Stability of Noncharacteristic Viscous Boundary Layers JO - Journées équations aux dérivées partielles PY - 2006 SP - 1 EP - 82 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.28/ DO - 10.5802/jedp.28 LA - en ID - JEDP_2006____A1_0 ER -
%0 Journal Article %A Métivier, Guy %T Lecture notes : Stability of Noncharacteristic Viscous Boundary Layers %J Journées équations aux dérivées partielles %D 2006 %P 1-82 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.28/ %R 10.5802/jedp.28 %G en %F JEDP_2006____A1_0
Métivier, Guy. Lecture notes : Stability of Noncharacteristic Viscous Boundary Layers. Journées équations aux dérivées partielles (2006), article no. 1, 82 p. doi : 10.5802/jedp.28. http://www.numdam.org/articles/10.5802/jedp.28/
[BBB] Bardos C., Brezis D. and Brezis H., Perturbations singulières et prolongement maximaux d’opérateurs positifs, Arch.Rational Mech. Anal., 53 (1973), pp 69–100. | Zbl
[BaRa] Bardos C. and Rauch J., Maximal positive boundary value problems as limits of singular perturbation problems, Trans. Amer.Math.Soc., 270 (1982), pp 377–408. | MR | Zbl
[Bon] Bony J-M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sc. E.N.S. Paris, 14 (1981) pp 209–246. | Numdam | MR | Zbl
[ChPi] Chazarain J. and Piriou, A., Introduction to the Theory of Linear Partial Differential Equations, North Holland, Amsterdam, 1982. | MR | Zbl
[GaZu] Gardner R. and Zumbrun K., The gap lemma and geometric criteria instability of viscous shock profiles, Comm. Pure Appl. Math, 51 (1998), pp 797–855. | MR | Zbl
[Gil] Gilbarg, D., The existence and limit behavior of the one-dimensional shock layer, Amer. J. Math. 73. 1951, 256-274. | MR | Zbl
[Gis] Gisclon M. Étude des conditions aux limites pour un système strictement hyperbolique, via l’approximation parabolique. J. Math. Pures Appl., 75 (1996), pp 485–508. | Zbl
[GiSe] Gisclon M. and Serre D., Étude des conditions aux limites pour un système strictement hyberbolique via l’approximation parabolique. C. R. Acad. Sci. Paris SÈr. I Math., 319 (1994), pp 377–382. | Zbl
[Goo] Goodman, J., Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Analysis 95. (1986), pp 325–344. | MR | Zbl
[GoXi] Goodman J. and Xin Z. Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rational Mech. Analysis 121 (1992), pp 235–265. | MR | Zbl
[GrGu] Grenier E. and Guè 0., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J.Diff.Equ., 143 (1998) pp 110–146. | MR | Zbl
[GrRo] Grenier E. and Rousset F., Stability of one dimensional boundary layers by using Green’s functions, Comm. Pure Appl. Math. 54 (2001), pp 1343–1385. | Zbl
[Gue1] Guès O., Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann.Inst.Fourier, 45 (1995) pp 973–1006. | Numdam | MR | Zbl
[Gue2] Guès O., Problème mixte hyperbolique quasilinéaire caractéristique, Comm. in Part.Diff.Equ., 15 (1990), pp 595–645. | MR | Zbl
[GMWZ1] Guès O., Métivier G., Williams M., and Zumbrun, K., Multidimensional viscous shocks I: degenerate symmetrizers and long time stability, Journal of the AMS, 18 (2005), pp 61-120 | MR | Zbl
[GMWZ2] Guès O., Métivier G., Williams M., and Zumbrun, K., Multidimensional viscous shocks II: the small viscosity problem, Comm. Pure and Appl. Math., 57 (2004) pp 141–218. | MR | Zbl
[GMWZ3] Guès O., Métivier G., Williams M., and Zumbrun, K., Existence and stability of multidimensional shock fronts in the vanishing viscosity limit, Arch.Rat.Mech.Anal., 175 (2005) pp 151–244. | MR | Zbl
[GMWZ4] Guès O., Métivier G., Williams M., and Zumbrun, K., Navier-Stokes regularization of multidimensional Euler shocks, Ann. Scient. Ec. Norm. Sup., to appear. | Numdam | MR | Zbl
[GMWZ5] Guès O., Métivier G., Williams M., and Zumbrun, K., Nonclassical multidimensional viscous and inviscid shocks, preprint
[GMWZ6] Guès O., Métivier G., Williams M., and Zumbrun, K., Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities, preprint
[GMWZ7] Guès O., Métivier G., Williams M., and Zumbrun, K., Uniform stability estimates for constant-coefficient symmetric hyperbolic boundary value problems, Comm. in Partial Diff. Equ., to appear | MR | Zbl
[GMWZ8] Guès O., Métivier G., Williams M., and Zumbrun, K., Stability of noncharacteristic boundary layers for the compressible Navier-Stokes and MHD equations, in preparation.
[GuWi] Gues O. and Williams M., Curved shocks as viscous limits: a boundary problem approach, Indiana Univ. Math. J., 51 (2002), pp 421-450. | MR | Zbl
[HoZu] Hoff D. and Zumbrun K., Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ. Math. J., 44 (1995), pp 603–676. | MR | Zbl
[KaS1] Kawashima S. and Shizutz Y., Systems of equations of hyperbolic-parabolic type, with applications to the discrete Boltzmann equations, Hokkaido Math.J., 14 (1985) pp 249–275. | MR | Zbl
[KaS2] Kawashima S. and Shizutz Y, On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tohoku Math.J., 40 (1988) pp 449–464 | MR | Zbl
[Kre] Kreiss H.O., Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), pp. 277-298. | MR | Zbl
[Lio] Lions J.L., Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lectures Notes in Math., 323, Sringer Verlag, 1973. | MR | Zbl
[Maj1] Majda A., The stability of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., n 275, 1983. | MR | Zbl
[Maj2] Majda A., The Existence of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., n 281, 1983. | MR | Zbl
[MaOs] Majda A., and Osher S., Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math., 28 (1975), pp 607-676. | MR | Zbl
[MaPe] Majda, A. and Pego, R., Stable viscosity matrices for systems of conservation laws, J. Diff. Eq., 56. (1985), pp 229-262. | MR | Zbl
[Mal] Malgrange B., Ideals of differentiable functions, Oxford Univ. Press, 1966. | MR | Zbl
[Mét1] Métivier G., Stability of multidimensional weak shocks, Comm., Partial Diff. Eq., 15 (1990), pp 983-1028. | MR | Zbl
[Mét2] Métivier G., The Block Structure Condition for Symmetric Hyperbolic Problems, Bull. London Math.Soc., 32 (2000), pp 689–702 | MR | Zbl
[Mét3] Métivier G, Stability of multidimensional shocks. Advances in the theory of shock waves, 25–103, Progr. Nonlinear Differential Equations Appl., 47, Birkhäuser Boston, Boston, MA, 2001. | MR | Zbl
[Mét4] Métivier G., Small Viscosity and Boundary Layer Methods, Birkhäuser, Boston 2004. | MR | Zbl
[MéZu1] Métivier G. and - Zumbrun K., Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems, Memoirs AMS, 826 (2005). | Zbl
[MéZu2] Métivier G. and - Zumbrun K., Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities, J. Diff. Equ., 211 (2005) pp 61-134. | MR | Zbl
[MéZu3] Métivier G. and - Zumbrun K., Symmetrizers and continuity of stable subspaces for parabolic–hyperbolic boundary value problems. J. Dis. and Cont. Dyn. Sys., 11 (2004) pp 205-220. | MR | Zbl
[Peg] Pego R., Stable viscosities and shock profiles for systems of conservation laws, Trans. A.M.S., 282 (1984), pp 749-763. | MR | Zbl
[PlZu] Plaza R. and Zumbrun K., An Evans function approach to spectral stability of small-amplitude shock profiles, J. Disc. and Cont. Dyn. Sys. 10. (2004), pp 885–924. | MR | Zbl
[Ral] Ralston J., Note on a paper of Kreiss, Comm. Pure Appl. Math., 24 (1971), pp 759–762. | MR | Zbl
[Rau1] Rauch J., is a continuable initial condition for Kreiss’ mixed problems, Comm.Pure and Appl.Math., 25 (1972) pp 265–285. | Zbl
[Rau2] Rauch J., Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer.Math.Soc, 291 (1985), pp 167–185. | MR | Zbl
[Rou1] Rousset F., Inviscid boundary conditions and stability of viscous boundary layers, Asympt.Anal., 26 (2001) pp 285–306. | MR | Zbl
[Rou2] Rousset F., Viscous approximation of strong shocks of systems of conservation laws. SIAM J. Math. Anal. 35 (2003), pp 492–519. | MR | Zbl
[Shi] Shiota M., Nash Manifolds, Lectures Notes in Mathematics, 1269, Springer Verlag. | MR | Zbl
[Ser] Serre D., Sur la stabilité des couches limites de viscosité. Ann. Inst. Fourier (Grenoble) 51 (2001), pp 109–130. | Numdam | MR | Zbl
[Zum2] Zumbrun K., 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. | MR | Zbl
[Zum3] Zumbrun K. Stability of large-amplitude shock waves of compressible Navier–Stokes equations. For Handbook of Fluid Mechanics III, S.Friedlander, D.Serre ed., Elsevier North Holland (2004). | MR
[ZuHo] Zumbrun K. and Howard P., Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J., 47 (1998), pp 741–871. | MR | Zbl
[ZuSe] Zumbrun K. and Serre D., Viscous and inviscid stability of multidimensional planar shock fronts , Indiana Univ. Math. J., 48 (1999), pp 937–992. | MR | Zbl
Cited by Sources: