LIST OF SELECTED
PUBLICATIONS OF
GEORGE JAIANI
(Other
transcriptions: Dzhaiani, Dzaiani)
1.
On the Deflections of Thin Wedge-shaped Shells,
Bulletin of the Academy of Science of the Georgian SSR, Vol. 65, 3, pp.
543-546, 1972 (in Russian, Georgian and English summaries)
2.
On One Problem of an Elastic Wedge-shaped Body,
Bulletin of the Academy of Science of the Georgian SSR, Vol. 70, 3, pp.
557-560, 1973 (in Russian, Georgian and English summaries)
3.
On One Problem for the Fourth Order Degenerate
Equation, Bulletin of the Academy of Science of the Georgian SSR, Vol. 75, 1,
pp. 17-20, 1974 (in Russian, Georgian and English summaries)
4.
On a Wedge-shaped Body Arbitrary Loaded Along the
Cusped Edge, Bulletin of the Academy of Science of the Georgian SSR, Vol.75, 2,
pp. 309-312, 1974 (in Russian, Georgian and English summaries)
5.
Arbitrary Loaded Elastic Half-plane Whose Young's
Modulus is Power Function of Depth, Materials of the I All-union School in
Theory and Numerical Methods in Shell and Plate Theory, Tbilisi University
Press, pp. 351-361, 1975 (in Russian)
6.
On a Wedge-shaped Shell, Proceedings of X All-union
Conference in Shell and Plate Theory,
7.
Riquier Problems with Weight for a Fourth Order
Degenerate Equation, Dokl., Akad. Nauk SSSR, Tom 231, 6, pp. 1285-1288, 1976
(in Russian), Riquier Problems with Weight for a Certain Degenerate Equation of
Fourth Order, Soviet Math. Dokl., Vol.17, 6, pp. 1715- 1719, 1976
8.
A Generalization of the Poisson Formula in Case of a
Half-plane for a Degenerate Equation of Even Order, Dokl. Akad.Nauk SSSR, Tom
235, N 6, pp. 1245-1248, 1977 (in
Russian), A Generalization of the Half-plane Poisson Formula for a Degenerate
Equation of Even Order, Soviet Math.Dokl.Vol.18, 4, pp.1132-1135,
1977
9.
Bending of a Plate with Power Law Changing Stiffness,
Annuaire Des Ecoles Superieures Mechanique Technique, Vol.XII,
2,
pp.15-19, 1977 (in Russian)
10. The Riquier Problem
for a Degenerate Equation, Complex Analysis and its Applications, Papers
Dedicated to I.Vekua‘s 70-th Anniversary, Moscow: Nauka Press, pp. 209-216,
1978 (in Russian)
11. On Some Boundary
Value Problems for Prismatic Cusped Shells, in Theory of Shells, Koiter W.T.
and Mikhailov G.K., Eds., North-Holland Pub.Comp., pp. 339-343, 1980
12. On a Physical
Interpretation of Fichera's Function, Acad.Naz.dei Lincei, Rend.della
Sc.Fis.Mat.e Nat., S. VIII, Vol.LXVIII, fasc.5, pp. 426-435, 1980
13. The Problem V for
the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua Institute of
Applied Mathematics, Vol.15, pp.77-83, 1981 (in Russian)
14. Solution of some
Problems for a Degenerate Elliptic Equation of Higher Order and their
Applications to Prismatic Shells, Tbilisi University Press, 1982 (in Russian,
Georgian and English summaries)
15. Euler-Poisson-Darboux
Equation, Tbilisi University Press, 1984 (in Russian, Georgian and English
summaries)
16. Boundary Value
Problems of Mathematical Theory of Prismatic Shells with Cusps, Proceedings of
All-union Seminar in Theory and Numerical Methods in Shell and Plate Theory,
Tbilisi University Press, pp.126-142, 1984 (in Russian)
17. Problems with
Discontinuous Boundary Conditions for the Euler-Poisson-Darboux Equation,
Reports of Seminar of I.Vekua Institute of Applied Mathematics, Vol.18,
pp.74-77, 1984 (in Russian)
18. Approximate
Solution of Boundary Value Problems in the Case of the Euler-Poisson-Darboux
Equation, Reports of Seminar of I.Vekua Institute of Applied Mathematics,
Vol.18, pp.78-82, 1984 (in Russian)
19. On the Behaviour of
a Solution of the Vekua Problem for the Euler-Poisson-Darboux Equation in the
Half-plane, Reports of Seminar of I.Vekua Institute of Applied Mathematics,
Vol.19, pp.23-26, 1985 (in Russian)
20. Formulas of Schwarz
Type for a Singular Differential Equation, Bulletin of the Academy of Sciences
of the Georgian SSR, Vol.122, N 3, pp.469-472, 1986
(in Russian, Georgian and English summaries)
21. On the Influence of
Coefficients of Junior Terms on Posing of Boundary Value Problems for Elliptic
Equations with Order Degeneration, Reports of Enlarged Sessions of the Seminar
of I.Vekua Institute of Applied Mathematics, Vol.2, N
1,
pp.31-34, 1986 (in Russian)
22. The Weighted
Dirichlet Problem with Discontinuous Boundary Data for the
Euler-Poisson-Darboux Equation in a Half-Plane, Proceedings of I.Vekua
Institute of Applied Mathematics, Vol.19, pp.38-59, 1987 (in Russian)
23. Weight Boundary
Value Problems for a Linear Degenerate Elliptic Equation of Second Order,
Uspekhi Matematichskikh Nauk, Vol.42, 4 (256), p.174, 1987 (in Russian)
24. Bending of
Prismatic Cusped Shell With Power Law Changing Stiffness, Proceedings of the
XIV All-union Conference in Shell and Plate theory, Tbilisi University Press,
pp.474-479, 1987 (in Russian)
25. Linear Elliptic
Equations with Order Degeneration and Prismatic Shells with Cusps, Proceedings
of All-union Conference in Modern Problems of Mathematical Physics, Tbilisi
University Press, Vol.1, pp.207-213, 1987 (in Russian)
26. The First Boundary Value
Problem of Cusped Prismatic Shell Theory in Zero Approximation of Vekua Theory,
Proceedings of I.Vekua Institute of Applied Mathematics, Vol.29, pp.5-38, 1988
(in Russian, Georgian and English summaries)
27. On the Problem of
Behaviour of Solutions of Boundary Value Problems in the Neighbourhood of
Discontinuity Points of Boundary Data, Reports of Enlarged Sessions of the
Seminar of I.Vekua Institute of Applied Mathematics, Vol.4, 1, pp.34-37, 1989
28. On a Way of
Construction of Solutions of Boundary Value Problems for Higher Order
Equations, Rendiconti di Matematica, Serie VII, Vol.10, pp.717-731, 1990
29. The Generalized
Holmgren Problem for the Equation yDu+buy=0 in the Case of a Half-circle,
Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied
Mathematics of Tbilisi State University, Vol.6, 1, pp.21-24, 1991
30. On Some
Applications of Variational Methods in the Theory of Bending of Prismatic
Cusped Shells, Proceedings of I.Vekua Institute of Applied Mathematics of
Tbilisi State University, Vol.47, pp.36-44, 1992
31. An Example of
Non-unique Solvability of Fichera Problem in the Classical Sense, Reports of
Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of
Tbilisi State University, Vol.8, 1, pp.31-34,1993
32. On a Way of
Solution of BVPs for a Class of Third Order Partial Differential Equations,
Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied
Mathematics of Tbilisi State University, Vol.10, 1, pp. 32-35, 1995
33. On a Generalization
of the Keldysh Theorem, Georgian Mathematical Journal, Vol.2, 3, pp.291-297,
1995
34. Elastic Bodies with
Non-smooth Boundaries – Cusped Plates and Shells, Zeitschrift fuer Angewandte
Mathematik und Mechanik, Vol.76, Supplement 2, pp.117-120, 1996
35. The Main Boundary
Value Problems of Bending of Cusped Plate in Weighted Sobolev Spaces, Applied
Mathematics and Informatics, Vol. 1, No.1, pp. 78-84, 1996
36. On a Modification
of the Lax-Milgram Theorem, Reports of Enlarged Session of the Seminar of
I.Vekua Institute of Applied Mathematics of Tbilisi State University , Vol.12,
1, pp.5-8, 1997
37. On Boundary Value
Problems for Conjugate Generalized Harmonic Functions, Ricerche di Matematica,
Vol. 47, fasc. 2, pp. 231-256, 1998
38. On a Model of a Bar
with Variable Thickness, BULLETIN of TICMI, Vol.2, pp.36-40, 1998 (for
electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
39. On a Cylindrical
Bending of a Prismatic Shell with Two Cusped Edges Under Action of an Idial
Fluid, BULLETIN of TICMI, Vol.2, pp.30-34, 1998 (coauthor N. Chinchaladze, for
electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
40. Bending of an
Orthotropic Cusped Plate, Appl. Math. Inform., Vol. 4, No. 1, pp. 29-65, 1999
41. Initial and
Boundary Value Problems for Singular Differential Equations and Applications to
the Theory of Cusped Bars and Plates, Complex methods for partial differential
equations (ISAAC Serials, Vol. 6), Eds.: H. Begehr, O. Celebi, W. Tutschke. Kluwer, Dordrecht, pp.113-149, 1999
42. Oscillation of an
Orthotropic Cusped Plate, Reports of Enlarged Session of the Seminar of I.Vekua
Institute of Applied Mathematics of
43. On a Vibration of
an Elastic Cusped Bar, BULLETIN of TICMI, Vol.4, pp. 24-28, 2000 (coauthor
S.Kharibegashvili, for electronic version see:
http://www.viam.science.tsu.ge/others/ticmi)
44. The First Boundary
Value Problem for the System of Cusped Prismatic Shells in the First
Approximation, Appl. Math. Inform., Vol.5, No. 2, pp. 26-46, 2000 (with: G.
Devdariani, S. Kharibegashvili, D. Natroshvili)
45. On a Mathematical
Model of Bars with Variable Rectangular Cross-sections, ZAMM-Zeitschrift fuer
Angewandte Mathematik und Mechanik, Vol.81, 3, pp.147-173, 2001
46. Application of
Vekua's Dimension Reduction Method to Cusped Plates and Bars, Bull. TICMI
(Tbilisi International Centre of Mathematics and Informatics), Vol.5, pp.
27-34, 2001 (for electronic version see:
http://www.viam.science.tsu.ge/others/ticmi)
47. Dynamical Problems
in the (0,0) and (1,0) Approximations of a Mathematical Model of Bars. In
"Functional-Analytic and complex Methods, Interactions, and Applications
to PDEs". Proceedings of the International Graz Workshop, Graz, Austria,
12-16 February 2001, World Scientific, pp.188-248, 2001 (with S.S. Kharibegashvili)
48. On a Cusped Elastic
Solid-Fluid Interaction Problem, Appl. Math. Inform, Vol. 6, No 2, pp. 25-64,
2001 (Coauthor N. Chinchaladze)
49. Static and
Dynamical Problems for a Cusped Beam, Proceedings of I.Vekua Institute of
Applied Mathematics of Tbilisi State University, Vol. 52, pp. 1-36, 2002
50. Theory of Cusped
Euler-Bernoulli Beams and Kirchoff-Love Plates, Lecture Notes of TICMI, vol.3,
2002 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
51. Relation of
Hierarchical Models of Cusped Elastic Plates and Beams to the Three-dimensional
Models, Reports of the Seminar of I.Vekua Institute of Applied Mathematics, 28,
31-39, 2002
52. Hierarchical Models
for Elastic Cusped Plates and Beams, Lecture Notes of TICMI, vol.4, 2003 (with:
S. Kharibegashvili, D. Natroshvili, W.L. Wendland, for electronic version see:
http://www.viam.science.tsu.ge/others/ticmi)
53. Bending of a Cusped
Plates on an Elastic Foundation, Bulletin of TICMI, Vol. 8, pp. 22-31, 2004
(for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
54. Mathematical Models
of Mechanics of Continua,
55. Two-dimensional
Hierarchical Models for Prismatic Shells with Thickness Vanishing at the
Boundary, Journal of Elasticity, Vol. 77, No. 2, 95-122, 2004 (with:
S. Kharibegashvili, D. Natroshvili, W.L. Wendland)
56. On Big Deflections
of Cusped Plates, Bulletin of TICMI, Vol. 9, 6-13, 2005 (with: N. Chinchaladze)
57. Oscillation of
Cusped Euler-Bernoulli Beams and Kirchhoff-Love Plates, Hacettepe Journal of
Mathematics and Statistics, Vol. 35 (1), 7-53, 2006 (with: A. Kufner)
58. A Cusped Prismatic
Shell-like Body under the Action of
Concentrated Moments, ZAMP-Zeitschrift fuer Angewandte Mathematik und
Physik (DOI 10.1007/s 00033-006-6005-7, Online First, published online: 20
November, 2006, access: http://www.birkhauser.ch)
59. A cusped Prismatic Shell-like Body
with the Angular Projection under the Action of a Concentrated Force,
Rendiconti Academia Nazionale delle Scienze detta dei XL, Memorie di Matematica
e Applicazioni, 124 0 (2006), Vol. XXX, facs. 1, 65-82, 65-82
60. Some Degenerate
Elliptic Systems and Applications to Cusped Plates, Mathematische Nachrichten,
280, 4, 388-407, 2007 (with B.-Wolfgang Schulze)
61. On Physical and Mathematical Moments
and the Setting of Boundary Conditions for Cusped Prismatic Shells and Beams,
Proceedings of the IUTAM Symposium on Relation of Shell, plate, Beam, and 3D
Models Dedicated to Centenary of Ilia Vekua, 23-27 April, 2007, Tbilisi,
Georgia. IUTAM Bookseries, Vol. 9, 133-146, Editors G. Jaiani, P. Podio-Guidugli. Springer, 2008
62. On a Nonlocal Boundary Value problem
for a System of Singular Differential Equations, Applicable Analysis: An International Journal, Volume 87, No. 1, 83 – 97, 2008;
First published electronically on 19 December 2007, (DOI:
10.1080/00036810701729964, access: http://www.tandf.co.uk/journals/titles/00036811.asp)
63. Existence and Uniqueness Theorems
for Cusped Prismatic Shells in the N-th Hierarchical Model, Mathematical
Methods in Applied Sciences, Vol. 31, No. 11, 1345-1367, 2008 (with N.
Chinchaladze, R. Gilbert, G. Jaiani, S. Kharibegashvili, D. Natroshvili, DOI 10.1002/mma.975, access for electronic version: http://www3.interscience.wiley.com/search/allsearch?mode=viewselected&product=journal&ID=117905390&
view_selected.x=111&view_selected.y=7, Published Online: 4 Feb 2008)
1.
Cylindrical
Bending of a Cusped Plate with Big Deflections, Journal of Mathematical
Sciences, Volume 157, Number 1, 52-69, Springer,
2009, [Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary
Mathematics and Its Applications), Vol. 51, Differential Equations and Their
Applications, 2008] (with N. Chinchaladze) access: http://www.springerlink.com/content/bt22900q5v238682/?p=1af5abb4d88148f9b5c7775b1319afab&pi=2