Geodesic
Asymptotic Integration of Linear Parabolic Problems with High-Frequency Coefficients in the Critical Case
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 522-538

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For a linear second-order parabolic equation with high-frequency coefficients, the complete asymptotics of time-periodic solutions is constructed and justified. The limit averaged stationary problem is assumed degenerate.
Keywords: linear second-order parabolic equation, parabolic equation with high-frequency coefficients, asymptotics of time-periodic solutions, Dirichlet problem, boundary layer method, semigroup, spectral projection. 
@article{MZM_2014_96_4_a4,
     author = {V. B. Levenshtam},
     title = {Asymptotic {Integration} of {Linear} {Parabolic} {Problems} with {High-Frequency} {Coefficients} in the {Critical} {Case}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {522--538},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a4/}
}
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V. B. Levenshtam. Asymptotic Integration of Linear Parabolic Problems with High-Frequency Coefficients in the Critical Case. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 522-538. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a4/