The talk will present some recent advances concerning the uniqueness and stability of solutions to nonlinear hyperbolic systems of conservation laws. First, some aspects of the front tracking algorithm and of the Glimm scheme will be discussed. I shall then explain the construction of a Lyapunov functional which controls the L^1 distance between couples of solutions, thus obtaining a uniform stability result. In turn, this yields a general uniqueness theorems for entropy weak solutions. The talk will be concluded by pointing out some open problems and research directions.

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Helge Holden <holden@math.ntnu.no>

2000-10-09 09:10