Buch, Englisch, Band 152, 264 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 575 g
Buch, Englisch, Band 152, 264 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 575 g
Reihe: Applied Mathematical Sciences
ISBN: 978-3-642-62797-2
Verlag: Springer
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included.
"It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet
"I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc.
"Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
1 Introduction.- 1.1 Notes.- 2 Scalar Conservation Laws.- 2.1 Entropy Conditions.- 2.2 The Riemann Problem.- 2.3 Front Tracking.- 2.4 Existence and Uniqueness.- 2.5 Notes.- 3 A Short Course in Difference Methods.- 3.1 ConservativeMethods.- 3.2 Error Estimates.- 3.3 APriori Error Estimates.- 3.4 Measure-Valued Solutions.- 3.5 Notes.- 4 Multidimensional Scalar Conservation Laws.- 4.1 Dimensional SplittingMethods.- 4.2 Dimensional Splitting and Front Tracking.- 4.3 Convergence Rates.- 4.4 Operator Splitting: Diffusion.- 4.5 Operator Splitting: Source.- 4.6 Notes.- 5 The Riemann Problem for Systems.- 5.1 Hyperbolicity and Some Examples.- 5.2 Rarefaction Waves.- 5.3 The Hugoniot Locus: The Shock Curves.- 5.4 The Entropy Condition.- 5.5 The Solution of the Riemann Problem.- 5.6 Notes.- 6 Existence of Solutions of the Cauchy Problem.- 6.1 Front Tracking for Systems.- 6.2 Convergence.- 6.3 Notes.- 7 Well-Posedness of the Cauchy Problem.- 7.1 Stability.- 7.2 Uniqueness.- 7.3 Notes.- A Total Variation, Compactness, etc.- A.1 Notes.- B The Method of Vanishing Viscosity.- B.1 Notes.- C Answers and Hints.- References.
