Krasnoshchok M. V.
Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 494-511
We consider an evolution free-boundary problem for a stationary linear system of the theory of elasticity that arises in the investigation of solid thin films in microelectronic devices. We prove its solvability on an arbitrary time interval under the condition that the initial data are sufficiently close to the stationary solution.
Classical Solvability of the First Initial Boundary-Value Problem for a Nonlinear Strongly Degenerate Parabolic Equation
Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1299-1320
We prove the existence of a classical solution global in time for the first initial boundary-value problem for a nonlinear strongly degenerate parabolic equation.
Ukr. Mat. Zh. - 1996. - 48, № 9. - pp. 1155–1165
We formulate the filtration problem with free boundary as a problem with discontinuous nonlinearity for a degenerate elliptic or parabolic system. We prove that a solution of the Dirichlet problem exists in both cases. We study some qualitative properties of these solutions, e.g., the existence of “dead cores”.