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Small Viscosity and Boundary Layer Methods : Theory, Stability Analysis, and Applications - G. Metivier

Small Viscosity and Boundary Layer Methods

Theory, Stability Analysis, and Applications


Published: 10th December 2003
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This book is an introduction to the stability analysis of noncharacteristic boundary layers, emphasizing selected topics and developing mathematical tools relevant to the study of multidimensional problems. Boundary layers are present in problems from physics, engineering, mechanics, and fluid mechanics and typically appear for problems with small diffusion. Boundary layers also occur in free boundary value problems, particularly in the analysis of shock waves.

The main goal of this presentation is to provide basic tools for the understanding of multidimensional boundary layers for systems. Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, BKW methods, construction of profiles, introduction to the theory of Evansa (TM) functions, and energy methods with Kreissa (TM) symmetrizers.

Part I is devoted to linear and semilinear problems. For simplicity, the analysis restricts its attention to constant coefficients of systemic dissipative systems. An important feature of this section is the derivation of energy estimates independent of viscosity. Part II is a treatment of quasilinear problems; the equation that governs the rapid variation inside the layer is derived and subsequently studied, allowing for the examination of multidimensional stability of planar layers.

This monograph is a valuable text for researchers, practitioners, and graduate students in applied mathematics, mathematical physics, and engineering and will be a useful supplement for the study of mathematical models in the applied sciences. Prerequisites for the reader include standard courses in analysis, integration theory, and PDEs.

From the reviews: "The main aim of this book is to provide a self-contained introduction to the topic together with a large exposition of the recent results ! . The book is very well written with an interesting level of difficulty which makes it easy to read. It is recommended to everyone interested in this area, beginners and specialists, since it starts with a good introduction and the presentation of rather simple results and finishes with a nice exposition of current research." (Frederic Rousset, Mathematical Reviews, Issue 2007 b)

List of Notation
Semiliear Layers Introduction and Example Hyperbolic Mixed Problems Hyperbolic-Parabolic Problems Semilinear Boundary Layers
Quasilinear Layers Quasilinear Boundary Layers: The Inner Layer O.D.E. Plane Wave Stability Stability Estimates Kreiss Symmetrizers for Hyperbolic-Parabolic Systems Linear and Nonlinear Stability of Quasilinear Boundary Layers
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780817633905
ISBN-10: 0817633901
Series: Modeling and Simulation in Science, Engineering and Technology
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 194
Published: 10th December 2003
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.08