| Small Viscosity and Boundary Layer Methods: Theory, Stability Analysis, and Applications 2004 Edition Contributor(s): Métivier, Guy (Author) |
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ISBN: 0817633901 ISBN-13: 9780817633905 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: December 2003 Annotation: 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 Evans? functions, and energy methods with Kreiss? 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. |
| Additional Information |
| BISAC Categories: - Science | Mechanics - Dynamics - Science | Physics - Mathematical & Computational - Mathematics | Applied |
| Dewey: 532.051 |
| LCCN: 2003062667 |
| Series: Modeling and Simulation in Science, Engineering and Technolo |
| Physical Information: 0.76" H x 6.46" W x 9.14" (1.06 lbs) 194 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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]). |