List of Main Publications of Otar Chkadua

  1. Differential properties of multidimensional hyper-singular integrals. (Russian) Trudy I. N. Vekua Inst. Prikl. Mat. (1977), 75-88.
  2. Investigation of the singular integro-differential operator in Rn. (Russian) Soobshch. Akad. Nauk Gruz. SSR 103 (1981), No. 3, 529-531 .
  3. Investigation of a singular integro-differential operator on a compact unbounded manifold.  (Russian) Soobshch. Akad. Nauk Gruz. SSR 107 (1982), No. 2, 249-252.
  4. Investigation of the basic problems of the couple-stress theory of elasticity for anisotropic media (with F. Hamza F). (Russian) Soobshch. Akad. Nauk Gruz. SSR 128 (1987), No. 3, 469-472.
  5. Mixed problems for homogeneous anisotropic elastic media (with D. Natroshvili and E. Shargorodsky). (Russian) Trudy I. N. Vekua Inst. Prikl. Mat. (1990), No. 2, 133-181.
  6. Investigation of basic mixed problems of couple- stress theory of elasticity for anisotropic media. Soobshch. Akad. Nauk Gruzii 152(1995), No. 3, 212-230.
  7. The nonclassical boundary-contact problems of elasticity for homogeneous anisotropic media. Math. Nachr. 172(1995), 64-79.
  8. The boundary-contact problems of elasticity for homogeneous media with a contact on some part of the boundaries. Georgian Math. J. 2(1995), No. 2, 111-122.
  9. Some boundary-contact problems of elasticity theory with mixed boundary conditions outside the contact surface. Math. Nachr. 188 (1997), 23-48.
  10. The Dirichlet, Neumann and mixed boundary value problems of the theory of elasticity in n-dimensional domains with boundaries containing closed cuspidal edges. Math. Nachr. 189(1998), 61-105.
  11. Asymptotics of solutions to some boundary value problems of elasticity for bodies with cuspidal edges (with R. Duduchava). Mem. Differential Equations Math. Phys. 15(1998), 29-58.
  12. Asymptotics of solutions to a pseudodifferential equations (with R. Duduchava). Bull. Georgian Acad. Sci. 158(1998), No. 2, 207-210.
  13.  Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotics (with R. Duduchava). Universität Stuttgart; Sonderforschung­bereich 404, Bericht 98/11, 1998, 1-69.
  14. Asymptotics of functions represented by potentials (with R. Duduchava). Universität Stuttgart; Sonderforschungbereich 404, Bericht 98/12, 1998, 1-47.
  15. Asymptotics of potential-type functions (with R. Duduchava). Bull. Georgian Acad. Sci. 159 (1999), No. 1, 23-27.
  16. Asymptotics of solutions to the crack problem (with R. Duduchava). Bull. Georgian Acad. Sci. 159 (1999), No. 3, 389-391.
  17. Boundary problems of thermopiezoelectricity in domains with cuspidal edges (with T. Buchukuri). Georgian Math. J. 7(2000), No. 3, 441-460.
  18. Asymptotics of functions represented by potentials (with R. Duduchava).  Russian J. Math. Physics 7(2000), No. 1, 15-47.
  19. Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotics (with R. Duduchava). Math. Nachr. 222(2001), 79–139.
  20. Solvability and asymptotics of solutions of crack-type boundary-contact problems of the couple-stress elasticity. Georgian Math. J. 10 (2003), No. 3, 427-465.

  21. Crack-type boundary value problems of electroelasticity (with T. Buchukuri and R. Duduchava). Oper. Theory Adv. Appl. 147 (2004), 189-212.

  22.  Mathematical modelling and analysis of interaction problems for piezoelectric composits. (with T. Buchukuri and D. Natroshvili). Rendiconti  Akademia Nazionale  delle Scienze detta dei  XL, Memorie di Matematika e Applicazioni  124 (2006), Vol  XXX fasc 1 pagg. 159-190.

  23. Boundary-value  problems  of  piezoelectricity  in  domains  with  cuts.(with  T. Buchukuri)         Mem.  Differential  equations  Math.  Phys. 38 (2006).    pp. 138-140.

  24. Boundary-value  dynamic problems of piezoelectricity in domains with cuts.(with  T.Buchukuri  and  R. Gachechiladze )  Mem. Differential  equations   Math.  Phys. 38 (2006).    pp. 135-137. 

  25. Wedge-type  boundary-contact dynamic  problems of elasticity.(with R. Gachechiladze)         Mem.   Differential  equations  Math.  Phys. 38 (2006).  pp. 150-153.

  26. About analysis of some localized boundary-domain integral equations for variable-coeffishient  BVPs. (with S. Mikhailov and D. Natroshvili).  Advances in Boundary Integral Methods—Proceedings of the 6-th  UK Conference on Boundary Integral Methods.2007,  pp. 291-302. Durham University Publ., UK.

  27. Mathematical problems for piezoelectric-metallic composits: existence and stress singularity analysis. (with  T. Buchukuri  and D. Natroshvili ). Proceedings of Waves 2007, pp. 323-327. 8-th International Conference on Mathematical and Numerical  Aspects of Waves. University of  Reading.

  28. Mathematical modeling and analysis of interaction problems for metallic-piezoelectric composite structure with regard to thermal stresses. (with T. Buchukuri and D. Natroshvili) . Universität Stuttgart, berichte aus dem Institut fuur Angewandte Analysis und Numerische Simulation. Preprint 2006/005,  pp.1-65.

  29. Interaction problems of metallic and piezoelectric materials with regard to thermal stresses     (with T. Buchukuri, D. Natroshvili, A.-M. Sändig ). Mem. Differential Equations Math. Phys. 45 (2008),  7-74.

  30. Crack-Type Boundary Value Problems in Mindlins Theory of Piezoelectricity. (with T. Buchukuri)  Georgian  Math.  J.  15  (2008),   No. 3,  455-473.

  31. Mixed Boundary Value Problems of Thermopiezoelectricity for Solids with Interior Cracks (with T. buchukuri and D. Natroshvili ).   Integral Equations Operator Theory, 64 (2009), No. 4, 495-537.

  32. Solvability and regularity results to boundary-transmission problems for metallic and piezoelectric elastic materials (with T. Buchukuri, D. Natroshvili and A.-M. Sändig). Math.  Nachr. 282 (2009),  No. 8, 1079-1110.

  33. Analysis of some localized boundary-domain integral equations (with S. Mikhailov and D. Natroshvili).   J. Integral Equations Appl.  21  (2009), No. 3,  407-447.

  34. Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I. Equivalence and Invertibility  (with S. Mikhailov and D. Natroshvili).  J. Integral Equations Appl. 21  (2009), No. 4, 499-543.

  35. Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. II. Solution Regularity and Asymptotics. (with S. Mikhailov and D. Natroshvili).  J. Integral Equations Appl. 22  (2010),  No. 1, 19-37.

  36. Stress Singularity analysis in Interface Crack Problems for Composite Structures. (with T. Buchukuri, D. Natroshvili). Proceedings of 7-th EUROMECH Solid Mechanics Conference, Lisbon, Portugal, 7-11 September, 2009, pp.1-20.

  37. Analysis of some  boundary-domain integral equations for variable-coefficient problems with cracks. (with S. Mikhailov and D. Natroshvili).  Advances in Boundary Integral Methods—Proceedings of the 7-th  UK Conference on Boundary Integral Methods. 2009,  pp. 37-51. Nottingham University Publ., UK.

  38. Interface Cracks Problems in Composites with Piezoelectric and Thermal Effects (with   T. Buchukuri, R. Duduchava, and D. Natroshvili).Proceedings of ASME  International Mechanical Engineering Congress & Exposition  IMECE 2009, Florida, USA, Vol. 10, PTS A and B,  pp. 821-830.

  39. Localized Boundary-Domain Integral Equations Formulation for Mixed Type Problems (with S. E. Mikhailov and D. Natroshvili).   Georgian Math. J. 17 (2010), No. 3, 69-494.

  40. Analysis of Segregated Boundary-Domain Integral Equations for Variable-Coefficient Problems with Cracks. (with S.E. Mikhailov and D. Natroshvili).  Numerical Methods for Partial Differential Equations (NMPDE) 27 (2011), No. 1, 121-140.

  41. Localized Direct Segregated Boundary-Domain Integral Equations for Variable Coefficient Transmission Problems with Interface Crack. (with S.E. Mikhailov and D. Natroshvili). Mem. Differential Equations Math. Phys. 52 (2011), 17-64.  Dedicated to the 120-th birthday anniversary of academician N. Muskhelishvili.

  42. Analysis of Some Localized Boundary-Domain Integral Equations for Transmission Problems with Variable Coefficients. (with S.E. Mikhailov and D. Natroshvili). Integral Methods in Science and Engineering. Computational and Analysis Aspects, C. Constanda and P. Harris (eds.), Chapter 11,  Springer 2011, pp. 91-108.

  43. Localized Boundary-Domain Integral Equations Method for Interface Crack Problem. (with S.E. Mikhailov and D. Natroshvili). Proceedings of 8-th UK Conference on Boudary Integral Methods. Leeds University  Press, Leeds,UK,4-5 July, 2011,  pp.49-56.

  44. Localized Boundary-Domain Integral Equations Method for Dirichlet Problem for Second Order Elliptic Equations with Matrix Variable Coefficients. (with S.E. Mikhailov and D. Natroshvili). Proceedings of 8-th UK Conference on Boundary Integral Methods. Leeds University  Press, Leeds,UK,4-5 July, 2011,  pp.119-126.

  45. Analysis of Segregated Boundary-Domain Integral Equations for Mixed Variable Coefficient BVPs in Exterior Domains  (with S.E. Mikhailov and D. Natroshvili ).  Integral Methods in Science and Engineering: Computational and Analysis Aspects, C. Constanda and P. Harris (eds.), Chapter 11, Springer 2011, pp.109-127. 

  46. Localized boundary-domain integral equations method for the Dirichlet boundary value problems for second order elliptic equations with variable coefficients. (with S.E. Mikhailov and D. Natroshvili ). Proc. A. Razmadze Math. Inst. 155 (2011), 100-102.

  47. Analysis of Direct Segregated Boundary-Domain Integral Equations for Variable Coefficient Mixed BVPs in Exterior Domains. (with S.E. Mikhailov and D. Natroshvili ). Anal. Appl. 10 (2012),  No. 4, 1-29.

  48. The screen type boundary value problems for anisotropic pseudo-Maxwell’s equations. (with R. Duduchava and D. Kapanadze).  Proc. A. Razmadze Math. Inst. 159  (2012).

  49. Potential methods for anisotropic pseudo-Maxwell’s equations in screen type problems. (with R. Duduchava and D. Kapanadze),  excepted for publication in Operator Theory: Advances and Applications.

  50. Localized boundary-domain integral equations approach for the Dirichlet boundary value problems for second order strongly elliptic systems with variable coefficients. (with S.E. Mikhailov and D. Natroshvili). Proc. A. Razmadze Math. Inst.  159 (2012), 1-15.

  51. Interface crack problems for metallic-piezoelectric composite structures. (with  T. Buchukuri, R. Duduchava and D. Natroshvil). Monograph, published in  Mem. Differential Equations Math. Phys. 56  (2012), 1-150.