An irregular conjugation problem for the system of the parabolic equations in the holder space

Abstract

We consider the conjugation problem for the system of parabolicequations with two small parameters �> 0, �> 0 in the boundary conditions.There are proved the existence, uniqueness and uniform coercive estimates ofthe solution with respect to the small parameters in the Holder space. Thisproblem is linearized one of the nonlinear problem with the free boundary ofFlorin type and it is in the base of the proof of the solidified of this nonlinearproblem in the Holder space.We study the problem with the free boundary of the Florin type in the Holder space