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Information × Registration Number 0209U008413, 0104U000860 , R & D reports Title Free boundary problems, nonlinear degenerate parabolic and elliptic equations, problems of existence and nonexistence of solutions, properties of singular solutions. popup.stage_title Head Tedeev Anatoliy Fedorovich, Registration Date 25-03-2009 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 Objects of investigation are well posedness and qualitative properties of boundary problems for quasilinear and nonlinear degenerate parabolic and elliptic equations, nonlinear free boundary problems. There were received new results in classic solvability of non stationary free boundary problems for elliptic equations which were founded on the research of nonstandard boundary problems with contains derivative in time on the boundary condition. Additional difficulties arise in the studying of that problem when the unknown boundary contains the corner points and with the glance of the curvature of the free boundary. There were described sufficient conditions of the existence of the "waiting time" for solutions of similar problems. There were explored free boundary problems, which contain elliptic-hyperbolic system of equations and simulate some biologic processes. There was given description of smoothness of solution's support boundary in regularity of initial data terms for the initial boundary problemsfor nonlinear degenerate parabolic equations. For quasilinear doubly degenerate parabolic equations with non-local source term the Fujita type theorem was received. The similar result was obtained for quasilinear doubly degenerate parabolic equations with the source term for a slowly decay initial data. There was established the criteria of tending to the zero of the total mass of a solution of the Neumann problem for quasilinear doubly degenerate parabolic equations with damping gradient term. The universal bounds near the blow-up time for the quasilinear doubly degenerate parabolic equation with the source term were established. The similar problem was investigated for equations with inhomogeneous density. For solutions of quasilinear elliptic and parabolic equations both the Wiener criteria and theorems of singularity's removability were proved. There were found precise conditions of instantaneous support compactification for doubly nonlinear parabolic equations with the strong absorption. Product Description popup.authors popup.nrat_date 2020-04-02 Close