Front Tracking for Hyperbolic Conservation Laws

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 This book presents the theory of hyperbolic conservation laws from basic theory to the forefront of research. The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking. The extension to multidimensional scalar conservation laws is obtained using dimensional splitting. The book includes detailed discussion of the recent proof of well-posedness of the Cauchy problem for one-dimensional hyperbolic conservation laws, and a chapter on traditional finite difference methods for hyperbolic conservation laws with error estimates and a section on measure valued solutions. Front Matter....Pages i-xii Introduction....Pages 1-21 Scalar Conservation Laws....Pages 23-62 A Short Course in Difference Methods....Pages 63-116 Multidimensional Scalar Conservation Laws....Pages 117-162 The Riemann Problem for Systems....Pages 163-204 Existence of Solutions of the Cauchy Problem for Systems....Pages 205-231 Well-Posedness of the Cauchy Problem for Systems....Pages 233-286 Back Matter....Pages 287-364 1. Introduction -- 2. Scalar Conservation Laws -- 3. A Short Course In Difference Methods -- 4. Multidimensional Scalar Conservation Laws -- 5. The Riemann Problem For Systems -- 6. Existence Of Solutions Of The Cauchy Problem -- 7. Well-posedness Of The Cauchy Problem. Helge Holden, Nils Henrik Risebro. Includes Bibliographical References (p. [351]-359) And Index.