Unlimited boundary regimes for quasilinear parabolic boundary-value problems with absorption (Q2735914)

Parabolic equations of second order are considered. Conditions guaranteeing appearance of localization and boundedness of solutions are obtained for generalized parabolic equations with double degeneration, if the boundary function is peaking as well as in the case of very ``strong'' absorption. The conditions on regularity of the boundary function for such problems are decreased. Results on boundedness of solutions for the mixed problem for some generalization of the heat equation for regimes with peaking are obtained as well. These results make it possible to investigate some properties of different parabolic equations.