Homogenization of diffusion equation with scalar hysteresis operator
The paper deals with a scalar diffusion equation where is a Prandtl-Ishlinskii operator and are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic...