On parabolic boundary value problems with a small parameter on the derivatives with respect to $t$

Conditions are obtained of the type in Tikhonov's theorem which, when satisfied, make possible passage to the limit on the small parameter $\varepsilon$. Estimates in Hölder 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 $\varepsilon\to0$ 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.