R. E. Showalter
University of Texas

Title: Partial Differential Equations with Hysteresis

We consider various nonlinear initial-boundary-value problems for partial differential equations with memory effects of hysteresis type. Several examples and numerical results are described. These include a general porous-medium equation or scalar conservation law with a hysteresis term distributed over the spatial region or dynamic boundary conditions that model hysteresis phenomena. It is shown that the dynamics of such problems are frequently determined by a contraction semigroup in appropriate product spaces.