# Faculty Profiles

## Kiguradze, Tariel

### 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

### Current 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

### 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.