Hysteresis in conservation laws: modeling, analysis, and simulation

In mathematical modeling, we call hysteresis the input-output relationship which depends on the input's history in a rate-independent way. Hysteresis is well-known in ferromagnetism but is also important in porous media, phase transitions, mathematical biology, plasticity theory, economic models and more.  This talk will focus on a scalar conservation law modeling gas transport with adsorption hysteresis. We will discuss approximation of the hysteresis functional which combines differential equations under constraints, diophantine approximations, and statistical mechanics; our approach is more practical than, e.g.,  the well-known Preisach model.  We discuss well-posedness of the model(s), stability of numerical scheme(s), as well as simulation results.  This is joint work with Ralph Showalter and others to be named in the talk.

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