Professor Jondo Gvazava

(2.X.1939 - 27. II. 2013)


 

Education and Scientific Degree:

1957 - 1962 Student of Tbilisi State University, Faculty of Mechanics and Mathematics
1962 Diploma with honour in Mathematics
1962 - 1965 Post-graduate student of Novosibirsk State University
1967 Ph.D. in Mathematics, Mathematical Institute of the Siberian Division 
of the Academy of Sciences of USSR
1970 Associated professor, Highest Certifying Commision of USSR
1972 Senior Scientific Researcher, Presidium of the Academy of Sciences of USSR
1981  Doctor of Mathematics, Highes Certifying Commision of USSR
1990 Professor in Differential Equations, The Highers Certifying Commision of USSR

 

Languages:

Georgian, Russian, German, English

 

Positions Held and Academic Experience:

1965 Assistant of the Department of Function Theory of Novosibirsk State University
1965 - 1967 Junior Scientific Researcher of the Department of Function Theory at 
Mathematical Institute of Syberian Division of the Academy of Sciences of USSR
1967 - 1972 Senior Scientific Researcher of the same department
1972 - 1986 Senior Scientific Researcher of the Department of Equations  of
Mathematical Physics at A. Razmadze Mathematical Institute of Georgian Academy of Sciences
1986 - 2000 Leading Scientific Researcher of the same department
2000 - 2013 Leading Scientific Researcher of the Department of Differential Equations at
A. Razmadze Mathematical Institute of Georgian Academy of Sciences

 

Parts Time Positions:

1965 - 1967 Assistant of the Department of "Function Theory" at Novosibirsk State University
1965 - 1973 Assosiated professor at the same department 
1973 - 1983 Associated professor of the Department of "Differential and Integral 
Equations" at Tbilisi State University
1983 - 1989 Professor of the Department of Applied Mathematics at the same University
1989 - 1992 Professor of Abkhazian State University
1990 - present Professor of the Department of Applied Mathematics at Georgian 

 

Research Areas:

Nonlinear hyperbolic equations; 
Quasilinear degenerated hyperbolic and mixed type equations;
Boundary initial and characteristic problems for linear, semilinear and quasilinear equations of 
different type

 

List of Main Publications

  1. A contribution to the theorie of boundary value problems for the equations ym+uxx+ uyy = k(x,y)eu in the large. (Russian) Dokl. Akad. Nauk SSSR 167(1966), 274-277; English transl.: Sov. Math., Dokl. 7(1966), 364-367.
  2. On the theory of boundary value problems for a class of quasilinear elliptic equations degenerate on the boundary. (Russian) Differentsial'nye Uravneniya 2(1966), 24-32; German transl: Differ. Equations 2(1966), 11-15.
  3. Global solution of the Tricomi problem for a class of nonlinear differential equations of mixed type. (Russian) Differentsial'nye Uravneniya 3(1967), 3-10.
  4. On uniqueness of solution of the Tricomi problem for a class of nonlinear equations. (Russian) Dokl. Akad. Nauk SSSR 190(1970), 259-262; English transl.: Sov. Math., Dokl. 11(1970), 65-69.
  5. Some estimates of the magnitude of solutions of nonlinear equations of mixed type. (Russian) Differentsial'nye Uravneniya 6(1970), 50-55.
  6. Some estimates for equations of mixed type. (Russian) Differentsial'nye Uravneniya 8(1972), 17-23.
  7. Some estimates of the magnitude of solutions of nonlinear equations of mixed type. Differential Equations 6(1972), 40-44.
  8. Some estimates for equations of mixed type. Differential Equations 8(1972), 12-16.
  9. The solutions of elliptic equations that are degenerate on the boundary of the domain. (Russian) Differentsial'nye Uravneniya 9(1973), 18-24.
  10. Solutions of elliptic equations degenerate on the boundary. Differential Equations 9(1974), 13- 17.
  11. The Cauchy problem for a certain quasilinear degenerate equation. (Russian) Differentsial'nye Uravneniya 13(1977), 29-35.
  12. On the global solvability of the Cauchy problem for a nonlinear equation. (Russian) Soobshch. Akad. Nauk Gruz. SSR 99(1980), 553-556.
  13. Global solution of the Cauchy problem for a certain quasilinear degenerate hyperbolic equation by method of characteristics. (Russian) Differentsial'nye Uravneniya 17(1981), 39-45.
  14. On some classes of quasilinear equations of mixed type. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 67(1981), 1-93.
  15. Global solution of Cauchy's problem for a degenerate quasilinear hyperbolic equation by the method of characteristics. Differential Equations 17(1981), 25-30.
  16. A modified Goursat problem for a degenerate second-order quasilinear hyperbolic equation. (Russian) Differentsial'nye Uravneniya 18(1982), 285-290; English transl.: Differ. Equations 18(1982), 230-233.
  17. Problems with initial and characteristic conditions for hyperbolic equations with nonlinear principal parts. (Russian) Differentsial'nye Uravneniya 19(1983), No. 1, 22-27; English transl.: Differ. Equations 19(1983), 18-21.
  18. On the Cauchy problem for an equation of surface theory. (Russian) Differentsial'nye Uravneniya i Primenen. 34(1983), 9-15.
  19. On second order nonlinear equations with complete characteristic systems and characteristic problems for them. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 87(1987), 45-53.
  20. On the general integral of a class of nonlinear equations and its applications. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 90(1988), 68-75.
  21. Some classes of hyperbolic equations and equations of mixed type. (Georgian) Metsniereba, Tbilisi, 1992, 1-176.
  22. On the initial Cauchy problem for a quasilinear degenerate hyperbolic equation. (Russian) Proc. A. Razmadze Math. Inst. 100(1992), 59-65.
  23.  Application of the general integral of a nonlinear equation with real characteristics in the investigation of Cauchy and Darboux problem. (Russian) Proc. A. Razmadze Math. Inst. 105(1995), 39-45.
  24. To the theory of boundary value problems for hyperbolic type equations and systems (with S. Kharibegashvili). Mem. Differential Equations Math. Phys. 12(1997), 68-75.
  25. On second order nonlinear equations with rectilinear characteristics. Georgian Math. J. 7(2000), No. 2, 299-319.
  26. General solutions and initial characteristic problems for second order nonlinear equations with rectilinear characteristics. (Russian) Liet. Mat. Rink. 40(2000), No. 4, 459-474; English trasl.: Lithuanian Math. J. 40(2000)(2001), No. 4, 352-363.
  27. Nonlocal and initial problems for quasilinear, nonstrictly hyperbolic equations with general solutions represented by superposition of arbitrary functions. Georgian Math. J. 10 (2003), no. 4, 687-707.
  28. The mean value property for nonstrictly hyperbolic second order quasilinear equations and the nonlocal problems. Proc. A. Razmadze Math. Inst. 135 (2004), 79-96.
  29. On one nonlinear version of characteristic problem with a free support of data. Proc. A. Razmadze Math. Inst. 140 (2006), 91-107.
  30. On mean-value property for hyperbolic equations. Proc. A. Razmadze Math. Inst. 155 (2011), 117-118. 
  31.  On hyperbolic equations with general integrals representable by superposition of arbitrary parameters, and characteristic problems. Proc. A. Razmadze Math. Inst. 159 (2012), 143-146. 
  32. On characteristic problems with a non-compact support of data. Proc. A. Razmadze Math. Inst. 162 (2013), 130-135 (with R. Bitsadze, G. Baghaturia and M. Menteshashvili). 
  33. Cauchy problem for a quasi-linear hyperbolic equation with closed support of data. Translated from Sovrem. Mat. Prilozh. Vol. 80, 2012, Part 1. J. Math. Sci. (N.Y.) 193 (2013), no. 3, 364-368 (with G. Baghaturia and M. Menteshashvili).