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S. P. Degtyarev

Publications and source records attributed to S. P. Degtyarev.

4 recordsLinked to original sources
arXiv2018

Classical solvability of the multidimensional free boundary problem for the thin film equation in the case of partial wetting

We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation in the case of partial wetting. We also obtain the Schauder estimates and solvability for the Dirichlet and the Neumann problem for a linear degenerate parabolic equation of fourth order. The final expanded version of this paper is available at AIMS Journals, Discrete and Continuous Dynamical Systems - A at http://aimsciences.org/article/doi/10.3934/dcds.2017156

math.AP↗
arXiv2016

On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions

We give relatively simple sufficient conditions on a Fourier multiplier, so that it maps functions with the H$\ddot{o}$lder property with respect to a part of the variables to functions with the H$o$lder property with respect to all variables. With the using of these sufficient conditions we prove the solvability in H$\ddot{o}$lder classes of the initial-boundary value problems for the linearized Cahn-Hilliard equation with dynamic boundary conditions of two types. For the solutions of these problems Schauder estimates are obtained. The final expanded version of this paper is available at AIMS Journals, Evolution Equations and Control Theory (EECT) at http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11870

math.AP↗
arXiv2015

Liouville property for solutions of the linearized degenerate thin film equation of fourth order in a halfspace

We consider a boundary value problem in the half-space for a linear parabolic equation of fourth order with a degeneration on the boundary of the half-space. The equation under consideration is substantially a linearized thin film equation. We prove that, if the right hand side of the equation and the boundary condition are polynomials in the tangential variables and time, the same property has any solution of a power growth. It is shown also that the specified property does not apply to normal variable. As an application, we present a theorem of uniqueness for the problem in the class of functions of power growth.

math.AP↗