Geodesic
The asymptotics of a~solution of a~parabolic equation as time increases without bound
Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1589-1610

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A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of $t^{-1}$ is constructed and substantiated. Bibliography: 8 titles.
Keywords: asymptotic expansion, small parameter, boundary-value problem, method of matching. 
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     author = {D. O. Degtyarev and A. M. Il'in},
     title = {The asymptotics of a~solution of a~parabolic equation as time increases without bound},
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D. O. Degtyarev; A. M. Il'in. The asymptotics of a~solution of a~parabolic equation as time increases without bound. Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1589-1610. http://geodesic.mathdoc.fr/item/SM_2012_203_11_a3/