Well-Posedness Theory for Hyperbolic Systems of Conservation Laws
The purpose of these lectures is to outline the main analytical ideas for the well-posedness theory based on nonlinear functionals. The first lecture gives a simple proof of theL- 1 contractionsemigroup property and introduces the Liu—Yang generalized entropy funtional for the scalar conservation law. Glimm’s interaction estimates and nonlinear functional for a general system are described in the second lecture. The third lecture illustrates the notion of wave tracing. The final lecture presents the L1-well posedness theory through the entropy functional. These lectures give an informal, intuitive presentation of the paper  of Tong Yang and the author.
The reader is also referred to this paper for the history of and references to the subject.
KeywordsShock Wave Generalize Entropy Rarefaction Wave Wave Pattern Riemann Problem
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