Logacheva O. Questions of the solvability and the behaviour of a solution to the Neumann problem for quasilinear parabolic equations with an absorption in domains with a noncompact boundary.

The thesis is devoted to the study of the Neumann problem for quasilinear degenerate parabolic equations in domains with a noncompact boundary. The behaviour of the solution of the second mixed problem for doubly nonlinear parabolic equations in dependence on the geometry of the domain is considered in the case of domains, narrowing at the infinity. Namely, sharp bilateral bounds of the maximum of the solution are obtained. The Neumann problem for quasilinear parabolic equations with absorption and a measure as initial data is considered in domains, expanding at the infinity. The existence and the non-existence of a weak solution in dependence on the absorption’s exponent are proved.