Homogenization of Diffusion Equation with Scalar Hysteresis Operator
نویسنده
چکیده
The paper deals with a scalar diffusion equation c ut = (F [ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f 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 data c and η when the spatial period ε tends to zero. The homogenized characteristics c∗ and η∗ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved.
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