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.

• YellowSale2006
• conservation laws
• front tracking
• hyperbolic partial differential equations
• Cauchy problem
• conservation law
• convergence
• differential equation
• hyperbolic partial differential equation
• Mathematica
• measure
• nonlinear partial differential equation
• numerical method
• partial differential equation
• solution
• stability

From the reviews:

"The book under review provides a self-contained, thorough, and modern account of the mathematical theory of hyperbolic conservation laws. … gives a detailed treatment of the existence, uniqueness, and stability of solutions to a single conservation law in several space dimensions and to systems in one dimension. This book … is a timely contribution since it summarizes recent and efficient solutions to the question of well-posedness. This book would serve as an excellent reference for a graduate course on nonlinear conservation laws … ." (M. Laforest, Computer Physics Communications, Vol. 155, 2003)

"The present book is an excellent compromise between theory and practice. Since it contains a lot of theorems, with full proofs, it is a true piece of mathematical analysis. On the other hand, it displays a lot of details and information about numerical approximation for the Cauchy problem. Thus it will be of interest for a wide audience. Students will appreciate the lively and accurate style … . this text is suitable for graduate courses in PDEs and numerical analysis." (Denis Serre, Mathematical Reviews, 2003 e)

• Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

  Helge Holden

• Department of Mathematics, University of Oslo, Oslo, Norway

  Nils Henrik Risebro

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