عنوان

Small Viscosity and Boundary Layer Methods

(Number (ISBN

9780817682149

(Number (ISBN

9781461264965

Number

b402590

Title Proper

Small Viscosity and Boundary Layer Methods

General Material Designation

[Book]

Other Title Information

Theory, Stability Analysis, and Applications /

First Statement of Responsibility

by Guy Métivier.

Place of Publication, Distribution, etc.

Boston, MA :

Name of Publisher, Distributor, etc.

Imprint: Birkhäuser,

Date of Publication, Distribution, etc.

2004.

Series Title

Modeling and Simulation in Science, Engineering and Technology,

ISSN of Series

2164-3679

Text of Note

I Semilinear Layers -- 1 Introduction and Example -- 2 Hyperbolic Mixed Problems -- 3 Hyperbolic-Parabolic Problems -- 4 Semilinear Boundary Layers -- II Quasilinear Layers -- 5 Quasilinear Boundary Layers: The Inner Layer ODE -- 6 Plane Wave Stability -- 7 Stability Estimates -- 8 Kreiss Symmetrizers for Hyperbolic-Parabolic Systems -- 9 Linear and Nonlinear Stability of Quasilinear Boundary Layers -- References.

0

Text of Note

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]).

International Standard Book Number

9781461264965

Title

Springer eBooks

Computer science-- Mathematics.

Differential equations, Partial.

Mathematical physics.

Mathematics.

Surfaces (Physics).

Métivier, Guy.

SpringerLink (Online service)

Date of Transaction

20190307162000.0

Electronic name

[Book]

Y