A Boundary Value Problem for a degenerate Moisture Transfer Equation with a Condition of the Third Kind

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2018.4.9164 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. 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 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 + References 1. Dzektser E. S. Equations of motion of free-surface underground water in layered media. Doklady Akademii Nauk SSSR [Doklady Mathematics], 1975, vol. 220, no. 3, pp. 540-543 (in Russian). 2. Rubinshtein L. I. On heat propagation in heterogeneous media. Izv. Akad. Nauk SSSR, Ser. Geogr. , 1948, vol. 12, no. 1, pp. 27-45 (in Russian). 3. Ting T. W. 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(in Russian). 14. Andreev V. B. On the convergence of difference schemes approximating the second and third boundary value problems for elliptic equations. USSR Comput. Math. Math. Phys. , 1968, vol. 8, no. 6, pp. 44-62. DOI: 10.1016/0041-5553(68)90092-X. 15. Samarskii A. A., Gulin A. V. Ustoichivost raznostnih shem [Stability of Finite Difference Schemes]. Moscow, Nauka, 1973, 416 p. (in Russian). The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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