# Tariel Kiguradze

**Associate Professor** | Mathematical Sciences

## Contact Information

## 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*

**(2010), No. 1, 29-46.**

**46** T. Kiguradze, On conditions of well-posedness of linear singular boundary value problems. *Differential Equations* ** 46** (2010), No2; translation from

*Differentsil’niye Uravneniya*

**(2010), No. 2, 183-190**

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

## 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