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Small Viscosity and Boundary Layer Methods

Theory, Stability Analysis, and Applications

  • Guy Métivier

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Semilinear Layers

    1. Front Matter
      Pages 1-1
    2. Guy Métivier
      Pages 3-20
    3. Guy Métivier
      Pages 21-50
    4. Guy Métivier
      Pages 51-78
    5. Guy Métivier
      Pages 79-93
  3. Quasilinear Layers

    1. Front Matter
      Pages 95-95
    2. Guy Métivier
      Pages 113-129
    3. Guy Métivier
      Pages 131-147
  4. Back Matter
    Pages 189-194

About this book

Introduction

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an intro­ duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl]. We consider parabolic singular perturbations of hyperbolic systems L(u) - £P(u) = 0, where L is a nonlinear hyperbolic first order system and P a nonlinear spatially elliptic term. The parameter e measures the strength of the diffusive effects. With obvious reference to fluid mechanics, it is referred to as a "viscosity." The equation holds on a domain n and is supplemented by boundary conditions on an.The main goal of this book is to studythe behavior of solutions as etends to O. In the interior of the domain, the diffusive effects are negligible and the nondiffusive or inviscid equations (s = 0) are good approximations. However, the diffusive effects remain important in a small vicinity of the boundary where they induce rapid fluctuations of the solution, called layers. Boundary layers occur in many problems in physics and mechanics. They also occur in free boundary value problems, and in particular in the analysis of shock waves. Indeed, our study of noncharacteristic boundary layers is strongly motivated by the analysis of multidimensional shock waves. At the least, it is a necessary preliminary and important step. We also recall the importance of the viscous approach in the theoretical analysis ofconservation laws (see, e.g., [Lax], (Kru], (Bi-Br]).

Keywords

Applied Mathematics Boundary value problem Derivation calculus equation function mathematical physics mathematics mechanics ordinary differential equation physics

Authors and affiliations

  • Guy Métivier
    • 1
  1. 1.MABUniversité de Bordeaux 1Talence CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8214-9
  • Copyright Information Birkhäuser Boston 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6496-5
  • Online ISBN 978-0-8176-8214-9
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site