Front Tracking for Hyperbolic Conservation Laws

Helge Holden is professor of mathematics at the Norwegian University of Science and Technology and an adjunct professor at the Center of Mathematics for Applications, part of the University of Oslo.  He has done extensive research in stochastic analysis, in particular in its application to flow in porous media.Nils Henrik Risebro is professor of mathematics at the University of Oslo. His research interests are mainly nonlinear partial differential equations and numerical methods for these. He has also worked on conservation laws with discontinuous coefficients in a variety of applications.

“This is the 2nd edition of the famous book … devoted to the modern theory of hyperbolic conservation laws. … The book is well written, well illustrated (it contains even cartoons) and may be recommended not only to experienced specialists in conservation laws but also to students specialized in this field.” (Evgeniy Panov, zbMATH 1346.35004, 2016)

• Preface.- Introduction.- Scalar Conservation Laws.- A Short Course in Difference Methods.- Multidimensional Scalar Conservation Laws.- The Riemann Problem for Systems.- Existence of Solutions of the Cauchy Problem.- Well-Posedness of the Cauchy Problem.- Conservation Laws with Discontinuous Flux Functions.- Total Variation, Compactness etc.- The Method of Vanishing Viscosity.- Answers and Hints.- Index.