Hysteresis in conservation laws: modeling, analysis, and simulation
- Thursday, February 18, 2021 from 3:00pm to 4:00pm
- Webex Meeting number: 120 608 6197, Password: applied
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.
- Department of Mathematical Sciences