ELLIPTIC-PARABOLIC EQUATIONS WITH HYSTERESIS BOUNDARY-CONDITIONS

A general porous-medium equation is uniquely solved subject to a pair of boundary conditions for the trace of the solution and a second func tion on the boundary. The use of maximal monotone graphs for the three nonlinearities permits not only the inclusion of the usual boundary c onditions of Dirichlet, Neumann, or Robin type, including variational inequality constraints of Signorini type, but also dynamic boundary co nditions and those that model hysteresis phenomena. It is shown that t he dynamic is determined by a contraction semigroup in a product of L( 1) spaces. Several examples and numerical results are described.