Homogenization of heat equation with hysteresis
This paper is devoted to the homogenization problem for the heat equation in a higher dimension in the form \[ (cu+W[u])_t-\text{div}(a\cdot \nabla u)=f,\tag{1} \] with scalar hypothesis operator \(W\) characterized by a coefficient \(\eta\). Here the coefficients \(c\), \(\eta\), \(a\) are spatially dependent. The authors prove that the solutions \(u^\varepsilon\) of \[ (c^\varepsilon u^\varepsilon+W^\varepsilon[u^\varepsilon])_t-\text{div}(a^\varepsilon\cdot\nabla u^\varepsilon)=f^\varepsilon \tag{2} \] with \(\varepsilon\)-periodic data converge to a solution \(u^*\) of a problem of the same form.
scientific article; zbMATH DE number 1882296