Educational Background

Master's Degree M. Lomonosov Moscow State University 1991

Ph.D. I. Javakhishvili Tbilisi State University, Georgia 1994

Professional Experience

Junior Researcher, I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 1991-1993

Assistant Professor of Mathematics, Department of Higher Mathematics, Faculty of Physics, I. Javakhishvili Tbilisi State University, 1993-1996

Associate Professor of Mathematics, Department of Higher Mathematics, Faculty of Physics, I. Javakhishvili Tbilisi State University, 1996-2003

Senior Researcher, A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 2000-2003

Associated Member, A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 2004-present

Associate Professor of Mathematics, Department of Mathematical Sciences, Florida Institute of Technology, 2004-present

Selected Publications

Research Monographs
T. Kiguradze, Some boundary value problems for systems of linear partial differential equations of hyperbolic type. Mem. Differential Equations Math.Phys. 1 (1994), 1-144.

Research Papers
T. Kiguradze, On a boundary value problem for quasilinear hyperbolic systems. (Russian) Dokl. Akad. Nauk 328 (1993), N 2, 135-138; translation in Russ. Acad. Sci. Dokl., Math. 47 (1993), N 1, 21-25.

T. Kiguradze, On bounded in a strip solutions of quasilinear partial differential equations of hyperbolic type. Appl. Anal. 58 (1995), N 3-4, 199-214.

T. Kiguradze, On periodic in the plane solutions of second order linear hyperbolic systems. Arch. Math. 33 (1997), N 4, 253-272.

T. Kiguradze, On periodic in the plane solutions of nonlinear hyperbolic equations. Nonlinear Anal. 39 (2000), N 2, Ser. A: Theory Methods, 173-185.

T. Kiguradze, On bounded and time-periodic solutions of nonlinear wave equations. J Math. Anal. Appl. 259 (2001), N 1, 253-276.

T. Kiguradze and I. P. Stavroulakis, On oscillatory properties of solutions of higher order linear hyperbolic equations. Advances Math. Sci. Appl. 11 (2001), N 2, 645-672.

T. Kiguradze and V. Lakshmikantham, On doubly periodic solutions of fourth order linear hyperbolic equations. Nonlinear Anal. Ser. A: Theory Methods. 49 (2002), N 1, 87-112.

T. Kiguradze and V. Lakshmikantham, On Dirichlet problem in a characteristic rectangle for higher order linear hyperbolic equations. Nonlinear Anal. Ser. A: Theory Methods 50 (2002), N 8, 1153-1178.

T. Kiguradze and I. P. Stavroulakis, On vanishing at infinity solutions of higher order linear hyperbolic equations. J. Inequalities Appl. 7 (2002), N 4, 517-553.

T. Kiguradze and T. Kusano, On well-posedness of initial-boundary value problems for higher order linear hyperbolic equations with two independent variables. (Russian) Differ. Uravn. 39 (2003), N 4, 516-526.

T. Kiguradze and T. Kusano, On ill-posed initial-boundary value problems for higher order linear hyperbolic equations with two independent variables. (Russian) Differ. Uravn. 39 (2003), N 9, 1379-1394.

T. Kiguradze and T. Kusano, On bounded and periodic in a strip solutions of nonlinear hyperbolic systems with two independent variables. Comput. and Math. 49 (2005), 335-364.

T. Kiguradze, Existence and uniqueness theorems on periodic solutions to multidimensional linear hyperbolic equations. Mem. Differential Equations Math. Phys. 36 (2005), 142-146.

T. Kiguradze and V. Lakshmikantham, On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order. J Math. Anal. Appl. 324 (2006), 1242-1261.

T. Kiguradze, On doubly periodic solutions of nonlinear hyperbolic equations of higher order. Georgian Math. J 14 (2007), N 3, 457-469.

I. Kiguradze and T. Kiguradze, On solvability of boundary value problems for higher order nonlinear hyperbolic equations. Nonlinear Anal. 69 (2008), 1914-1933.

T. Kiguradze, On solvability and well-posedness of boundary value problems for nonlinear hyperbolic equations of the fourth order. Georgian Math. J 15 (2008), N 3, 555-569.

T. Kiguradze, On solvability and unique solvability of two-point singular boundary value problems. Nonlinear Anal. 71 (2009), 789-798.

T. Kiguradze, On some nonlocal boundary value problems for linear singular differential equations of higher order. Mem. Differential Equations Math. Phys. 47 (2009), 169-174.

T. Kiguradze, The Vallée-Poussin Problem for Higher Order Nonlinear Hyperbolic Equations. Comput. and Math. 59 (2010), 994-1002.

T. Kiguradze, Estimates for the Cauchy function of linear singular differential equations and some applications. Differential Equations 46 (2010) No 1; translation from Differentsil’niye Uravneniya 46 (2010), No. 1, 29-46.

T. Kiguradze, On conditions of well-posedness of linear singular boundary value problems. Differential Equations 46 (2010), No2; translation from Differentsil’niye Uravneniya 46 (2010), No. 2, 183-190

I. Kiguradze, and T. Kiguradze, Optimal conditions of solvability of nonlocal problems for second-order ordinary differential equations. Nonlinear Anal. 74 (2011), 757-767.

I. Kiguradze, and T. Kiguradze, Conditions of well-posedness of nonlocal problems for higher order linear differential equations with singularities. Georgian Mathematical Journal 18 (2011), No. 4, 735-760.

I. Kiguradze, and T. Kiguradze, Conditions of well-posedness of nonlocal boundary value problems for second order linear differential equations. Differ Equ. 47 (2011), no. 10, 1414–1425. translation from Differentsil’niye Uravneniya 47 (2011), No. 10, 1400-1411.

T. Kiguradze, Conditional well-posedness of nonlocal problems for fourth order linear hyperbolic equations with singularities. Mem. Differential Equations Math. Phys. 54 (2011), 51-68.

T. Kiguradze, and R. Ben-Rabha, On strong well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations with two independent variables. Georgian Mathematical Journal 24 (2017), No. 3, 409-428.  

I. Kiguradze, and T. Kiguradze, Analog of the first Fredholm Theorem for higher order nonlinear differential equations.  Differ Equ. .53 (2017), no. 8, 1024-1032. translation from Differentsil’niye Uravneniya  53 (2017), No. 8, 996-1004. 

I. Kiguradze, and T. Kiguradze, Oscillation properties of higher order sublinear differential equations. Differ Equ..54 (2018), no. 12, 1545–1559. translation from Differentsil’niye Uravneniya 54 (2018), No. 12, 1589-1603.

I. Kiguradze, and T. Kiguradze, Oscillation criteria for higher order sublinear delay differential equations. Researches in Mathematics and Mechanics 23 (2018), 130-137.

T. Kiguradze, and N. Aljaber I. Kiguradze, and T. Kiguradze, Multidimensional periodic problems for higher order linear hyperbolic equations. Georgian Math. J. 26 (2019), No. 2, 235-256.

T. Kiguradze, and R. Alhuzally, On a two-dimensional Dirichlet type problem for a linear hyperbolic equation of fourth order. Georgian Math. J, 30 (2023), 1-19.

T. Kiguradze, N. Aljaber, and R. Ben-Rabha, Nonlocal boundary value problems for higher order nonlinear hyperbolic equations with two independent variables. Memoirs on Differential Equations and Mathematical Physics 90 (2023), 55-80.

Research

Nonlocal boundary value problems for higher order nonlinear hyperbolic equations with two independent variables

Periodic solutions of linear and quasilinear partial differential equations of higher order

Nonclassical boundary value problems for linear partial differential equations of higher order

Research & Project Interests

Oscillatory properties of solutions to nonlinear elliptic equations of Emden-Fowler type in unbounded conical domains (Diploma Thesis)

General initial-boundary value problems in a characteristic rectangle for linear hyperbolic systems with two independent variables (Ph.D. Thesis)

Bounded and time-periodic solutions of nonlinear wave equations

Asymptotic properties of solutions to higher order linear hyperbolic equations in an infinite strip

General initial-boundary value problems in a characteristic rectangle for higher order nonlinear hyperbolic equations; well-posed and ill-posed problems

Nonclassical boundary value problems for linear partial differential equations of higher order