Geodesic
The corner boundary layer in nonlinear singularly perturbed parabolic equations
Čebyševskij sbornik, Tome 13 (2012) no. 3, pp. 28-46

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The Dirichlet problem is considered for the nonlinear parabolic equation in a rectangle. The existence of the solution and its asymptotic expansion is proved. 
@article{CHEB_2012_13_3_a1,
     author = {I. V. Denisov and T. J. Denisova and A. V. Rodionov},
     title = {The corner boundary layer in nonlinear singularly perturbed parabolic equations},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {28--46},
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     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2012_13_3_a1/}
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I. V. Denisov; T. J. Denisova; A. V. Rodionov. The corner boundary layer in nonlinear singularly perturbed parabolic equations. Čebyševskij sbornik, Tome 13 (2012) no. 3, pp. 28-46. http://geodesic.mathdoc.fr/item/CHEB_2012_13_3_a1/