A numerical method for solving one nonlocal boundary value problem for a third-order hyperbolic equation

被引：0
作者：
M. Kh. Beshtokov
机构：
[1] Kabardino-Balkar State University,
来源：
Computational Mathematics and Mathematical Physics | 2014年 / 54卷
关键词：
boundary value problems; nonlocal condition; a priori estimate; difference scheme; stability and convergence of difference schemes; third-order hyperbolic equation; pseudo-parabolic equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A nonlocal boundary value problem for a third-order hyperbolic equation with variable coefficients is considered in the one- and multidimensional cases. A priori estimates for the nonlocal problem are obtained in the differential and difference formulations. The estimates imply the stability of the solution with respect to the initial data and the right-hand side on a layer and the convergence of the difference solution to the solution of the differential problem.
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页码：1441 / 1458
页数：17
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共 19 条
  • [1] Barenblat G I(1960)Basic concept in the theory of seepage of homogeneous liquids in fissured rocks J. Appl. Math. Mech. 25 852-864
  • [2] Zheltov Yu P(1975)Equations of motion of free-surface underground water in layered media Dokl. Akad. Nauk SSSR 220 540-543
  • [3] Kochina I N(1948)On heat propagation in heterogeneous media Izv. Akad. Nauk SSSR Ser. Geogr. 12 27-45
  • [4] Dzektser E S(1974)A cooling process according to two-temperature theory of heat conduction J. Math. Anal. Appl. 45 23-31
  • [5] Rubinshtein L I(1972)Pseudoparabolic equations in one space variable J. Differ. Equations 12 559-565
  • [6] Ting T W(1973)Integral operators and the first initial-boundary value problems for pseudoparabolic equations with analytic coefficients J. Differ. Equations 13 506-522
  • [7] Colton D L(2004)Boundary value problem with A. M. Nakhushev’s nonlocal condition for a pseudoparabolic moisture transfer equation Differ. Uravn. 18 280-285
  • [8] Colton D L(2004)On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation Differ. Equations 40 815-826
  • [9] Vodakhova V A(1982)On some boundary value problems for third-order equations arising in the modeling of flows in porous media Differ. Equations 18 689-699
  • [10] Kozhanov A I(1965)Instability, uniqueness, and nonexistence theorems for the equation on a strip Arch. Rat. Mech. Anal. 19 100-116
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