Geodesic
On parabolic boundary value problems with a~small parameter on the derivatives with respect to~$t$
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 287-302

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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. 
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     author = {V. G. Borisov},
     title = {On parabolic boundary value problems with a~small parameter on the derivatives with respect to~$t$},
     journal = {Sbornik. Mathematics},
     pages = {287--302},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/}
}
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V. G. Borisov. On parabolic boundary value problems with a~small parameter on the derivatives with respect to~$t$. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 287-302. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a1/