Geodesic
Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 917-934

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This paper is devoted to constructing an asymptotics of the solution to the Cauchy problem for a linear parabolic equation of second order with variable coefficients containing a small parameter at the highest derivative. Sufficient conditions for the existence and uniqueness of the “multiplicative” asymptotic expansion of the global solution of the problem are given. 
@article{MZM_2000_68_6_a12,
     author = {V. M. Khametov},
     title = {Asymptotics of the {Solution} to the {Cauchy} {Problem} for {Linear} {Parabolic} {Equations} of {Second} {Order} with {Small} {Diffusion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {917--934},
     publisher = {mathdoc},
     volume = {68},
     number = {6},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a12/}
}
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V. M. Khametov. Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 917-934. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a12/