Small Viscosity and Boundary Layer Methods: Theory, Stability Analysis, and Applications
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schriftenreihe: | Modeling and Simulation in Science, Engineering and Technology
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France) It is intended to serve as an introduction 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]) |
| Beschreibung: | 1 Online-Ressource (XXII, 194 p) |
| ISBN: | 9780817682149 9781461264965 |
| ISSN: | 2164-3679 |
| DOI: | 10.1007/978-0-8176-8214-9 |
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| id | DE-604.BV042419212 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817682149 9781461264965 |
| issn | 2164-3679 |
| language | English |
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| series2 | Modeling and Simulation in Science, Engineering and Technology |
| spelling | Métivier, Guy Verfasser aut Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications by Guy Métivier Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XXII, 194 p) txt rdacontent c rdamedia cr rdacarrier Modeling and Simulation in Science, Engineering and Technology 2164-3679 This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France) It is intended to serve as an introduction 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]) Mathematics Differential equations, partial Computer science / Mathematics Mathematical physics Surfaces (Physics) Partial Differential Equations Characterization and Evaluation of Materials Applications of Mathematics Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Informatik Mathematik Mathematische Physik https://doi.org/10.1007/978-0-8176-8214-9 Verlag Volltext |
| spellingShingle | Métivier, Guy Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications Mathematics Differential equations, partial Computer science / Mathematics Mathematical physics Surfaces (Physics) Partial Differential Equations Characterization and Evaluation of Materials Applications of Mathematics Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Informatik Mathematik Mathematische Physik |
| title | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications |
| title_auth | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications |
| title_exact_search | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications |
| title_full | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications by Guy Métivier |
| title_fullStr | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications by Guy Métivier |
| title_full_unstemmed | Small Viscosity and Boundary Layer Methods Theory, Stability Analysis, and Applications by Guy Métivier |
| title_short | Small Viscosity and Boundary Layer Methods |
| title_sort | small viscosity and boundary layer methods theory stability analysis and applications |
| title_sub | Theory, Stability Analysis, and Applications |
| topic | Mathematics Differential equations, partial Computer science / Mathematics Mathematical physics Surfaces (Physics) Partial Differential Equations Characterization and Evaluation of Materials Applications of Mathematics Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Informatik Mathematik Mathematische Physik |
| topic_facet | Mathematics Differential equations, partial Computer science / Mathematics Mathematical physics Surfaces (Physics) Partial Differential Equations Characterization and Evaluation of Materials Applications of Mathematics Computational Mathematics and Numerical Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Informatik Mathematik Mathematische Physik |
| url | https://doi.org/10.1007/978-0-8176-8214-9 |
| work_keys_str_mv | AT metivierguy smallviscosityandboundarylayermethodstheorystabilityanalysisandapplications |