Aghalaya S. Vatsala
Professor

Contact:
Office: 406 Maxim Doucet
Phone: 337-482-5274
E-mail: asv5357@louisiana.edu
Home page: http://www.ucs.louisiana.edu/~asv5357

Degrees:
Ph.D. 1973 Indian Institute of Technology, Madras
M.S. 1968 Bangalore University, Bangalore, India
B.S. 1966 Bangalore University, Bangalore, India

Statement:
My main areas of research are ordinary and partial differential equations. My primary focuses are in the study of impulsive differential equations, reaction diffusion equations, differential equations with delay, integro-differential equations, singular systems and its applications. We develop numerical iterative procedures (yielding faster convergence) for the computation of solutions. Lyapunov stability theory, and stability in terms of two measures for large scale dynamical systems are my other major interests.

Selected research publications:

• Impulsive Hybrid Fuzzy Differential Equations, Univesity of NIS, Facta Universitatis Series Mechanics, Automatic Control and Robotics, 3 (2003), 851-858.
• Set Differential Equations and Monotone Flows (with V. Lakshmikantham), Nonlinear Dynamics and Systems Theory, 3 (2003), 33-43.
• Interconnection Between Set and Fuzzy Differential Equations (with V. Lakshmikantham and S. Leela), Nonlinear Analysis, 54 (2003), 351-360.
• Practical Stability of Hybrid Impulsive Systems, Proceedings of the Fourth International Conference on Nonlinear Problems in Aviation and Aerospace, (2003), 519-525.
• Hybrid Systems on on Time Scales (with V. Lakshmikantham), Journal of Computational and Applied Mathematics, 141 (2002), 1-284.
• Extended Method of Quasilinearization for Reaction Diffusion Systems (with J. Vasundhara Devi), Proceedings of Neural, Parallel and Scientific Computation, 2 (2002), 273-276.
• Basic Theory of Fuzzy Differential Equations (with V. Lakshmikantham), Journal of Difference Equations and Applications, 8 (2002), 978-989.
• Setvalued Hybrid Differential Equations and Stability in Terms of Two Measures (with V. Lakshmikantham and S. Leela), International Journal of Hybrid Systems, 2, (2002), 169-187.
• Generalized Quasilinearization Method for Parabolic Integro-differential Equations (with Liwen Wang), Quarterly of Applied Mathematics, LIX (2001), 459 -470.
• Generalized Quasilinearization for Nonlinear Problems, (with V. Lakshmikantham), Kluwer Academic Publishers, (1998)
• Second Method of Lyapunov for Stability of Linear Impulsive Differential-Difference Equations with Variable Impulsive Perturbations (with D.D. Bainov and I.M.Stamova), Journal of Applied Math and Stochastic Analysis, 11 (1998), 209-216.
• Strict Stability Criteria for Dynamic Systems on Time Scales, Journal of Difference Equations and Applications, 3 (1998), 267-276.
• Variation of Parameters in Terms of Lyapunov-Like Functions and Stability of Perturbed Systems (with Xinzhi Liu), Nonlinear Studies, 5 (1998), 47-58.
• Generalized Quasilinearization for Impulsive reaction Diffusion Equations with Fixed Moments of Impulses (with Zahia Drici and Nader Kouhestani), Dynamic Systems and Applications, 7 (1998), 245-257.
• Generalized Quasilinearization for Systems of Reaction-Diffusion Equations (with Jiang Jiahui), Applied Math and Computation, 97 (1998), 223-235.
• The Origin of Mathematics (with V. Lakshmikantham), Nonlinear Studies, 5 (1998), 255-257.
• Stability of Moving Invariant Sets for Functional Differential Systems (with S.G. Deo), International Journal of Nonlinear Differential Equations, Theory, Methods and Applications, 3 (1997), 179-186.
• Stability of moving invariant sets, Nonlinear Dynamics, Advances in Nonlinear Dynamics (with V. Lakshmikantham), Stability and Control: Theory, Methods and Appl, 5 (1997), 79-83.
• Reaction Diffusion Equations and Quadratic Convergence (with H. Alkhaby and M. Mahrous), Journal of Applied Math and Stochastic Analysis, 10 (1997), 179-186.
• Generalized quasilinearization for impulsive differential equations with fixed moments of impulse (with J. Vasundara Devi, G. ChandraKala), Dynamics of Continuous, Discrete and Impulsive Systems, 1 (1995), 91-99.
• Quadratic and semi-quadratic convergence of IVP (with Donna Stutson), Neural Parallel Sci. Comput., 3 (1995), 235-248.
• Improved generalized quasilinearization method for second order boundary value problem (with N. Shahzad), Dynamic Systems Appl. 4 (1995), 79-86.
• Generalized quasilinearization and reaction diffusion equations, Nonlinear Times and Digest, 1 (1994), 211-220.
• Monotone Iterative Technique for Nonlinear Differential Equations (with G. S. Ladde and V.Lakshmikantham), (1985), Pitman Publishing Co.