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Nonlinear Conservation Laws and Divergence-Measure Fields

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If you have a question about this talk, please contact Prof. Clément Mouhot.

In this talk we will start with several mathematical challenges and fundamental issues we have to face for solving nonlinear hyperbolic conservation laws. Then we will analyse a class of weakly differentiable vector fields, called divergence-measure fields, and its natural connection with entropy solutions for hyperbolic conservation laws. In particular, we will discuss some recent efforts to establish a theory of divergence-measure fields toward developing analytical frameworks for studying entropy solutions of multidimensional hyperbolic conservation laws. Further connections, trends, and open problems in this direction will be also addressed.

This talk is part of the Partial Differential Equations seminar series.

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