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

doi:10.1016/S0252-9602(14)60115-6

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1695-1706.doi: 10.1016/S0252-9602(14)60115-6

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

A.S. BERDYSHEV, A. CABADA, B.Kh. TURMETOV

Department of Applied Mathematics and Informatics, Kazakh National Pedagogical University named after Abai, Almaty, Kazakhstan； Departmento de Analise Matematica, Facultade de Matematicas, University of Santiago de Compostela, Santiago de Compostela, Spain； Khoja Ahmet Yasawi International Kazakh-Turkish University, Kazakhstan

收稿日期:2013-09-13 修回日期:2014-05-03 出版日期:2014-11-20 发布日期:2014-11-20
基金资助:
The research of A.Cabada was partially supported by Ministerio de Ciencia e Innovacion-SPAIN, and FEDER, project MTM2010-15314 and research of A.S. Berdyshev and B.Kh. Turmetov was supported by the Ministry of Science and Education of the Republic of Kazakhstan through the Project No. 0713 GF.

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

A.S. BERDYSHEV, A. CABADA, B.Kh. TURMETOV

Department of Applied Mathematics and Informatics, Kazakh National Pedagogical University named after Abai, Almaty, Kazakhstan； Departmento de Analise Matematica, Facultade de Matematicas, University of Santiago de Compostela, Santiago de Compostela, Spain； Khoja Ahmet Yasawi International Kazakh-Turkish University, Kazakhstan

Received:2013-09-13 Revised:2014-05-03 Online:2014-11-20 Published:2014-11-20
Supported by:
The research of A.Cabada was partially supported by Ministerio de Ciencia e Innovacion-SPAIN, and FEDER, project MTM2010-15314 and research of A.S. Berdyshev and B.Kh. Turmetov was supported by the Ministry of Science and Education of the Republic of Kazakhstan through the Project No. 0713 GF.

摘要/Abstract

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.

关键词: biharmonic equation, boundary value problem, fractional derivative, the Riemann-Liouville operator

Abstract:

Key words: biharmonic equation, boundary value problem, fractional derivative, the Riemann-Liouville operator

中图分类号:

31A30

A.S. BERDYSHEV, A. CABADA, B.Kh. TURMETOV. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY#br# OPERATOR OF A FRACTIONAL ORDER[J]. 数学物理学报(英文版), 2014, 34(6): 1695-1706.

A.S. BERDYSHEV, A. CABADA, B.Kh. TURMETOV. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY[J]. Acta mathematica scientia,Series B, 2014, 34(6): 1695-1706.

参考文献

[1] Andersson L-E, Elfving T, Golub G H. Solution of biharmonic equations with application to radar imaging. J Comput Appl Math, 1998, 94(2): 153–180

[2] Lai M-C, Liu H-C. Fast direct solver for the biharmonic equation on a disk and its application to incom-pressible flows. Appl Math Comput, 2005, 164(3): 679–695

[3] Ehrlich L N, Gupta M M. Some difference schemes for the biharmonic equation. SIAM J Numer Anal, 1975, 12(5): 773–790

[4] Ali A H A, Raslan K R. Variational iteration method for solving biharmonic equations. Physics Letters A, 2007, 370(5/6): 441–448

[5] Bjorstad P. Fast numerical solution of the biharmonic Dirichlet problem on rectangles. SIAM J Numer Anal, 1983, 20: 59–71

[6] Dang Q A. Iterative method for solving the Neumann boundary problem for biharmonic type equation. J Comput Appl Math, 2006, 196(2): 634–643

[7] Shi Z, Cao Y-Y, Chen Q-J. Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method. Appl Math Model, 2012, 36(11): 5143–5161

[8] Deng Y, Li Y. Regularity of the solutions for nonlinear biharmonic equations in RN. Acta Math Sci, 2009, 29B(5): 1469–1480

[9] Begehr H. Dirichlet problems for the biharmonic equation. General Math, 2005, 13(2): 65–72

[10] Wang Y. Boundary Value Problems for Complex Partial Differential Equations in Fan-Shaped Domains[D]. Free University Berlin, 2010

[11] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. Math Studies, Vol 204. Elsevier, 2006

[12] Karachik V V, Turmetov B Kh, Torebek B T. On some integro-differential operators. In: The class of harmonic functions and their applications. Siberian Adv Math, 2012, 22(2): 115–134

[13] Karachik V V. Construction of polynomial solutions to some boundary value problems for poisson’s equa-tion. Comput Math Math Phys, 2011, 51(9): 1567–1587

[14] Karachik V V, Turmetov B Kh, Bekaeva A. Solvability conditions of the Neumann boundary value problem for the biharmonic equation in the unit ball. Int J Pure Appl Math, 2012, 81(3): 110–118

[15] Bavrin I I. Operators for harmonic functions and their applications. Differ Equ, 1985, 21(1): 9–15

[16] Kanguzhin B E, Koshanov B D. Necessary and sufficient conditions of solvability of boundary value problems for inhomogeneous polyharmonic equation in a ball. Ufa Math J, 2010, 2(2): 41–52 (in Russian)

[17] Kal’menov T S, Suragan D. On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation. Differ Equ, 2012, 48(3): 441–445

[18] Agmon S, Douglis A, Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm Pure Appl Math, 1959, 12(4): 623–727

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

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

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