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Field name	Details
Dewey Class	515.353
Title	Small Viscosity and Boundary Layer Methods ([EBook] :) : Theory, Stability Analysis, and Applications / / by Guy Métivier.
Author	Métivier, Guy
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 2004.
Physical Details	XXII, 194 p. : online resource.
Series	Modeling and Simulation in Science, Engineering and Technology 2164-3679
ISBN	9780817682149
Summary 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]).:
Contents 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8214-9
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Characterization and Evaluation of Materials . Computational Mathematics and Numerical Analysis . Computer mathematics . Engineering mathematics . Materials science . Mathematical Methods in Physics . Mathematics . Partial differential equations . Physics . Theoretical, Mathematical and Computational Physics . Authors: Métivier, Guy . Corporate Authors: SpringerLink (Online service) . Series: Modeling and Simulation in Science, Engineering and Technology . Classification: 515.353 . 515.353 (DDC 22) .

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Small Viscosity and Boundary Layer Methods: Theory, Stability Analysis, and Applications

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