ON PARABOLIC BOUNDARY VALUE PROBLEMS WITH A SMALL PARAMETER ON THE DERIVATIVES WITH RESPECT TO $ t$

Abstract

Conditions are obtained of the type in Tikhonov's theorem which, when satisfied, make possible passage to the limit on the small parameter . Estimates in Holder spaces of functions are obtained for the solution of the problem. The author determines how the rate of convergence of the solution to the limit function as depends on the smoothness of the functions contained in the equations and the boundary and initial conditions. Cases of both finite and infinite time intervals are considered.Bibliography: 14 titles.