Markasheva V. Regularity and asymptotic qualities of solutions of Cauchy problems for degenerate quasilinear parabolic equations with nonlinear Baouendi-Grushin type operator

The thesis is devoted to the investigation of Cauchy problems for quasilinear degenerate parabolic equations with nonlinear Baouendi-Grushin type operator. Local Holder continuity of a wide class of quasilinear parabolic equations with nonlinear Baouendi-Grushin type operator was established in terms of Carno-Caratheodory metric. The asymptotic behavior of solution of Cauchy problem for model quasilinear parabolic equation with Baouendi-Grushin type operator was investigated. Sharp conditions of the decay of a total mass of solution of Cauchy problem for the model quasilinear parabolic equation with Baouendi-Grushin type operator and gradient absorption with weigh was investigated.