A free boundary problem for a weak-coupled system (Q2735902)

A free boundary value problem for a weakly-coupled system with regeneration is considered. This problem appears in the simulation of various physical processes in double-porosity media. NEWLINENEWLINENEWLINELocal in time classical solvability of the indicated problem is proved. The method consists in localization technique and potential theory. Some uniform a priori estimates are obtained in a model boundary value problem for a parabolic equation with a small parameter \(\varepsilon\) by the derivative with respect to the time variable. The derivative with respect to time appears in the boundary condition also. Moreover, one considers the limit behaviour of the solution when \(\varepsilon\) tends to zero.