Geodesic
Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time
Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 3-16

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In this paper, we consider quasilinear parabolic equations which degenerate on a solution due to a multiplier of the derivative with respect to time. In the many-dimensional case, we prove the existence of a solution of a general boundary-value problem from a class of unbounded functions. Restrictions to nonlinearity of the multiplier of the derivative with respect to time are different from ones considered before by other authors. 
@article{DVMG_2007_7_1_a0,
     author = {E. G. Agapova},
     title = {Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a0/}
}
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E. G. Agapova. Solvability of nonlinear heat equation in class of unbounded functions with degeneration of coefficient near derivative with respect to time. Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a0/