Hyperbolic systems of conservation laws. (English) Zbl 0768.35059

Godlewski, Edwige; Raviart, Pierre-Arnaud

Mathématiques & Applications (Paris). 3-4. Paris: Ellipses, 252 p. (1991).

The monograph is restricted essentially to scalar conservation laws and is divided into four chapters, the first presenting some examples of conservation laws, weak solutions of systems of such laws and giving, also, a mathematical notion of entropy. Chapter II is devoted to the mathematical theory of the Cauchy problem for scalar conservation laws in several space dimensions. In chapter III explicit finite difference schemes for approximating scalar conservation laws are examined. In the last chapter the construction of such second order schemes is examined.
The presented material is an extended version of a one-semester post- graduate course in Numerical Analysis taught at the University P. et M. Curie and at the Ecole Polytechnique, both is Paris.

Reviewer: E.V.Nicolau (Bucureşti)

MSC:

35L65	Hyperbolic conservation laws
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99	Numerical methods for partial differential equations, boundary value problems
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations

Keywords:

scalar conservation laws; weak solutions; Cauchy problem; several space dimensions; finite difference schemes; second order schemes