Buch, Französisch, Englisch, 286 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 738 g
Hyperbolicity, Entropies, Shock Waves
Buch, Französisch, Englisch, 286 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 738 g
ISBN: 978-0-521-58233-9
Verlag: Cambridge University Press
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
Weitere Infos & Material
1. Some models; 2. Scalar equations in dimension d = 1; 3. Linear and quasi-linear systems; 4. Dimension d = 1, the Riemann problem; 5. Glimm's method; 6. Second order perturbations; 7. Viscosity profiles of shock waves; Bibliography; Index.
