Homogenization of heat equation with hysteresis

The contribution deals with heat equation in the form (cu + W[u])(t) = div(a (.) delu) + f, where the nonlinear functional operator W[u] is a Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function eta. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate-Sprekels. The homogenization problem for this equation is studied. For epsilon --> 0, a sequence of problems of the above type with spatially epsilon-periodic coefficients c(epsilon), eta(epsilon), alpha(epsilon) is considered. The coefficients c*, eta* and alpha* in the homogenized problem are identified and convergence of the corresponding solutions u(epsilon) to u* is proved. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.