Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems

Introduction Linear stability: the model case Pieces of paradifferential calculus $L^2$ and conormal estimates near the boundary Linear stability Nonlinear stability Appendix A. Kreiss symmetrizers Appendix B. Para-differential calculus Appendix Bibliography.

[1]  G. Métivier.  Interaction de deux chocs pour un système de deux lois de conservation, en dimension deux d'espace , 1986 .

[2]  H. Kreiss.  Initial boundary value problems for hyperbolic systems , 1970 .

[3]  Kevin Zumbrun,et al.  The gap lemma and geometric criteria for instability of viscous shock profiles , 1998 .

[4]  Jeffrey Rauch,et al.  BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one , 1986 .

[5]  Denis Serre,et al.  Conditions aux limites pour un système strictement hyperbolique fournies, par le schéma de Godunov , 1997 .

[6]  Jeffrey Rauch,et al.  Symmetric positive systems with boundary characteristic of constant multiplicity , 1985 .

[7]  Frederic Rousset,et al.  Stability of one‐dimensional boundary layers by using Green's functions , 2001 .

[8]  M. Balazard,et al.  REMARQUES SUR UN TH ´ EOR ` EME DE , 1989 .

[9]  A. Majda.  The stability of multi-dimensional shock fronts , 1983 .

[10]  K. Roberts,et al.  Thesis , 2002 .

[11]  K. Zumbrun.  Multidimensional Stability of Planar Viscous Shock Waves , 2001 .

[12]  李基炯,et al.  § 14 , 1982, Fichte.

[13]  Guy Métivier,et al.  Stability of Multidimensional Shocks , 2001 .

[14]  Christopher Jones,et al.  Stability of the travelling wave solution of the FitzHugh-Nagumo system , 1984 .

[15]  John Evans,et al.  Nerve Axon Equations: II Stability at Rest , 1972 .

[16]  John Evans.  Nerve Axon Equations: III Stability of the Nerve Impulse , 1972 .

[17]  J. Ralston.  Note on a paper of Kreiss , 1971 .

[18]  F. Rousset,et al.  Inviscid boundary conditions and stability of viscous boundary layers , 2001 .

[19]  Kevin Zumbrun,et al.  Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow , 1995 .

[20]  C. Bardos,et al.  Maximal positive boundary value problems as limits of singular perturbation problems , 1982 .

[21]  Kevin Zumbrun,et al.  Nonuniqueness of solutions of Riemann problems , 1996 .

[22]  Kevin Zumbrun,et al.  Pointwise semigroup methods and stability of viscous shock waves Indiana Univ , 1998 .

[23]  J. Bony,et al.  Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires , 1980 .

[24]  Emmanuel Grenier,et al.  Boundary Layers for Viscous Perturbations of Noncharacteristic Quasilinear Hyperbolic Problems , 1998 .

[25]  Kevin Zumbrun,et al.  Viscous and inviscid stability of multidimensional planar shock fronts , 1999 .

[26]  Michael I. Weinstein,et al.  Eigenvalues, and instabilities of solitary waves , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[27]  On the Stability of Traveling Waves in Weighted L∞ Spaces , 1994 .

[28]  F. Massey,et al.  Differentiability of solutions to hyperbolic initial-boundary value problems , 1974 .