Homogenization and two-scale convergence
SIAM Journal on Mathematical Analysis
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The contribution deals with heat equation in the form (c u + W[u])t = div(a . ∇u) + f, where the nonlinear functional operator W[u] is a Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function η. 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 ε → 0, a sequence of problems of the above type with spatially ε-periodic coefficients cε, ηε, aε is considered. The coefficients c*, η* and a* in the homogenized problem are identified and convergence of the corresponding solutions uε to u* is proved.