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Applied Math Seminar
An introduction to kinetic relations for undercompressive shocks
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This will be an introduction to the theory of undercompressive shock waves. I will explain the importance of small scale effects in solutions to systems of conservation laws arising in continuum physics. Undercompressive waves are fundamental in phase transition dynamics (van der Waals fluids, martensitic materials), especially when both viscosity and capillarity effects come into play. The proper selection of physically meaningful, discontinuous, entropy solutions requires the concept of a kinetic relation. |