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A Boundary Value Problem for a degenerate Moisture Transfer Equation with a Condition of the Third Kind
Beshtokov, M. Kh. , Kanchukoev V. Z. , Erzhibova F. A.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 4.
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 three-dimensional problem to one-dimensional 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.
Keywords: 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, pseudo-parabolic equation
Language: Russian Download the full text
For citation: Beshtokov M. KH., Kanchukoyev V. Z., Erzhibova F. A. A Boundary Value Problem for a degenerate Moisture Transfer Equation with a Condition of the Third Kind // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], 2017, vol. 19, no. 1, pp. 13-26. DOI 10.23671/VNC.2018.4.9164
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