The asymptotic expansion of solutions to quasilinear parabolic problems with the Dirichlet boundary condilions is constructed in the regions with a fine-grain boundary. It is shown that the sequence of the remainders of ...
A class of functions Bq,s is defined which contains generalized solutions to some higher order quasilinear parabolic equations. We prove that Bq,s is imbedded in the space of Holder functions.
We study the properties of solutions of weakly nonlinear parabolic equations in cylindrical domains. The existence conditions are established for local nontangential limits as t ? 0.