Martynenko A. Blow up for nonlinear degenerate parabolic equations with source term and inhomogeneous density

The thesis is devoted to the study the Cauchy problem for parabolic equations with a source term and inhomogeneous density. The conditions of existence and nonexistence of global solutions to the doubly nonlinear parabolic equations with inhomogeneous density and power source term were found for the first time. In case of the global in time solvability estimates of solutions for a large time were obtained. In the blow up case the estimate of solutions near the blow up time was obtained. The local Holder continuity of generalized solutions to a wide class of parabolic equations with inhomogeneous density was established.