Hyperbolic Systems of Conservation Laws
نویسنده
چکیده
Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions. 1-Review of basic theory. This chapter reviews the basic deenitions and properties of systems of conservation laws. For a comprehensive introduction to the theory of hyperbolic systems we refer to 22, 23, 24]. 1.1-Basic deenitions. A single conservation law in one space dimension is a rst order partial diierential equation of the form u t + f(u) x = 0: (1:1) Here u is the conserved quantity while f is the ux. Integrating (1.1) over the interval a; b] one 1
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