Small Viscosity and Boundary Layer Methods: Theory, Stability Analysis, and Applications (Modeling and Simulation in Science, Engineering and Technology) - Hardcover
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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]).
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Small Viscosity and Boundary Layer Methods
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -\* Metivier is an expert in the field of pdes/math physics, with a particular emphasis on shock waves.\*New monograph focuses on mathematical methods, models, and applications of boundary layers, present in many problems of physics, engineering, fluid mechanics. \* Metivier has good Birkhauser track record: one of the main authors of 'Advances in the Theory of Shock Waves' (Freistuehler/Szepessy, eds, 4187-4).\* Manuscript endorsed by N. Bellomo, MSSET series editor.should be a good sell to members of MSSET community, who by-in-large are based in Europe.\* Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems,WKB methods, construction of profiles, introduction to the theory of Evans' functions, and energy methods with Kreiss' symmetrizers. 220 pp. Englisch. Bestandsnummer des Verkäufers 9780817633905
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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Develops mathematical tools relevant to the study of multidimensional problemsUseful supplement for the study of mathematical models in the applied sciences* Metivier is an expert in the field of pdes/math physics, with a particular emp. Bestandsnummer des Verkäufers 5975385
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Small Viscosity and Boundary Layer Methods
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Birkhäuser, Birkhäuser Dez 2003, 2003
ISBN 10: 0817633901
ISBN 13: 9780817633905
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Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 220 pp. Englisch. Bestandsnummer des Verkäufers 9780817633905
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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]). Bestandsnummer des Verkäufers 9780817633905
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