ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

被引：26

作者：

Berdyshev, A. S. ^{[1
]}

Cabada, A. ^{[2
]}

Turmetov, B. Kh. ^{[3
]}

机构：

[1] Kazakh Natl Pedag Univ, Dept Appl Math & Informat, Alma Ata, Kazakhstan

[2] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela, Spain

[3] Khoja Ahmet Yasawi Int Kazakh Turkish Univ, Alma Ata, Kazakhstan

来源：

ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 06期

关键词：

biharmonic equation; boundary value problem; fractional derivative; the Riemann-Liouville operator; DIRICHLET PROBLEM;

D O I：

10.1016/S0252-9602(14)60115-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.

引用

页码：1695 / 1706

页数：12

共 18 条

[1] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].

AGMON, S ;

DOUGLIS, A ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) :623-727

[2] Variational iteration method for solving biharmonic equations [J].

Ali, A. H. A. ;

Raslan, K. R. .

PHYSICS LETTERS A, 2007, 370 (5-6) :441-448

[3] Solution of biharmonic equations with application to radar Imaging [J].

Andersson, LE ;

Elfving, T ;

Golub, GH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1998, 94 (02) :153-180

[4]

BAVRIN II, 1985, DIFF EQUAT+, V21, P6

[5]

Begehr H., 2005, General Mathematics, V13, P65

[6] FAST NUMERICAL-SOLUTION OF THE BIHARMONIC DIRICHLET PROBLEM ON RECTANGLES [J].

BJORSTAD, P .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (01) :59-71

[7] Iterative method for solving the Neumann boundary value problem for biharmonic type equation [J].

Dang, Quang A. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 196 (02) :634-643

[8] REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN RN [J].

Deng Yinbin ;

Li Yi .

ACTA MATHEMATICA SCIENTIA, 2009, 29 (05) :1469-1480

[9] SOME DIFFERENCE SCHEMES FOR BIHARMONIC EQUATION [J].

EHRLICH, LW ;

GUPTA, MM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (05) :773-790

[10] On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation [J].

Kal'menov, T. Sh. ;

Suragan, D. .

DIFFERENTIAL EQUATIONS, 2012, 48 (03) :441-445

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