
A boundary value problem for a degenerate moisture transfer equation with a condition of the third kind
M. KH. Beshtokov^{}, V. Z. Kanchukoyev^{}, F. A. Erzhibova^{} ^{} KabardinoBalkar State University after Kh. M. Berbekov, Nalchik, 360004, Russia
Abstract:
In this work, we study the pseudoparabolic equation
in the three dimensional space. The equation of this form implies
the presence of cylindrical or spherical symmetry that enables one to move from
a threedimensional problem to onedimensional problem, but with degeneration.
In this regard, we study the solvability and stability of solutions to boundary
value problems for degenerate pseudoparabolic equation of the third order of
general form with variable coefficients and third kind condition, as well as
difference schemes approximating this problem on uniform grids. The main result
consists in proving a priori estimates for a solution to both the
differential and difference problems by means of the method of energy
inequalities. The obtained inequalities imply stability of the solution relative
to initial data and right side. Because of the linearity of the considered
problems these inequalities allow us to state the convergence of the approximate
solution to the exact solution of the considered differential problem under the
assumption of the existence of the solutions in the class of sufficiently smooth
functions. On the test examples the numerical experiments are performed
confirming the theoretical results obtained in the work.
Key words:
equation with degeneration, boundary value problem, condition of the third kind, a priori estimate, difference scheme, stability and convergence of a difference scheme, moisture transfer equation, pseudoparabolic equation.
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UDC:
519.635 Received: 25.11.2015
Citation:
M. KH. Beshtokov, V. Z. Kanchukoyev, F. A. Erzhibova, “A boundary value problem for a degenerate moisture transfer equation with a condition of the third kind”, Vladikavkaz. Mat. Zh., 19:4 (2017), 13–26
Citation in format AMSBIB
\Bibitem{BesKanErz17}
\by M.~KH.~Beshtokov, V.~Z.~Kanchukoyev, F.~A.~Erzhibova
\paper A boundary value problem for a degenerate moisture transfer equation with a condition of the third kind
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 4
\pages 1326
\mathnet{http://mi.mathnet.ru/vmj629}
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