A homogenization result for a parabolic equation with Preisach hysteresis
Jana Kopfová · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2007
Abstract In this paper we consider an initial boundary value parabolic problem [cu + 𝒫[u]]_t ‐ div(a ċ ν u) = f, with Preisach hysteresis 𝒫. The functions c, a, and the density function ψ of the Preisach operator are allowed to depend also on the space variable x. The equation is homogenized by considering a sequence of equations with spatially periodic data cϵ, aϵ, and ψϵ, where the spatial period ϵ converges to 0. Properties of hysteresis operators and the concept of two‐scale convergence are used to show the convergence of the corresponding solutions to the solution of the homogenized problem.