Geodesic
Boundary value problems for linear parabolic equations degenerate on the boundary of a region
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 643-652.

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In the strip $\mathrm{Q\{\,0$ we consider a linear second-order parabolic equation which is degenerate on the boundary $\mathrm{t=0}$, $\mathrm{x=0}$. Assuming that the coefficient of the time derivative has a zero of a sufficiently high order at $\mathrm{t=0}$, we find the sufficient conditions to ensure the correctness of certain boundary value problems. One of these problems occurs in the theory of the temperature boundary layer. 
@article{MZM_1972_12_5_a19,
     author = {T. D. Dzhuraev},
     title = {Boundary value problems for linear parabolic equations degenerate on the boundary of a region},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--652},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a19/}
}
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T. D. Dzhuraev. Boundary value problems for linear parabolic equations degenerate on the boundary of a region. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 643-652. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a19/