Geodesic
Solvability boundary value problem for degenerate quasilinear parabolic equation in a~domain with nontube boundary
Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 63-73

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In this paper, we consider a quasilinear parabolic equation in nontube domain, which degenerate on a solution. We suppose the essential boundedness of the derivative of the function that define the curvilinear boundary, and prove an existence and uniqness theorems for the first boundary-value problem. We use compactness methods for functions from Banach space scale. At the Preliminary part establish abstract theorems about completeness certain system of function in nontube domain. 
@article{DVMG_2000_1_1_a8,
     author = {N. E. Istomina},
     title = {Solvability boundary value problem for degenerate quasilinear parabolic equation in a~domain with nontube boundary},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {63--73},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a8/}
}
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N. E. Istomina. Solvability boundary value problem for degenerate quasilinear parabolic equation in a~domain with nontube boundary. Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 63-73. http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a8/