Alexander Khapalov

Linear & Semilinear Partial Differential Equations $\bullet$ Control Theory

1. A class of a globally controllable semilinear heat equation with superlinear term, J. Math. Anal. Appl., 242, (2000), 271-283.

2. Exact null-controllability for the semilinear heat equation with superlinear nonlinear term and mobile internal controls, Nonlinear Analysis: Theory, Methods & Applications, 43, (2001), 785-801.

3. Bilinear system control and FACTS application (with R.R. Mohler), J. Opt. Th. Appl., Special Issue Honoring D.G. Luenberger, 105 (2000), 621-637.

4. Bilinear control for global controllability of the semilinear parabolic equation with superlinear term, In" Control of Nonl. Distr. Systems dedicated to David Russell,
   (Chen/Lasiecka/Zhou, Eds.), Marcel Decker, (2001), 139-155.

5. Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation, SIAM J. Contr. Opt., 40 (2001), 231-252.

6. Observability and stabilization for the one dimensional wave equation with bouncing point sensors and actuators, Mathematical Methods in Applied Sciences, 24, (2001), 1055-1072.

7. On bilinear controllability of the parabolic equation with the reaction-diffusion term satisfying Newton's Law, Special issue of Computational and Applied Mathematics, dedicated to the memory of J.-L. Lions, V. 21, (2002), pp. 1-23.

8. Global non-negative controllability of the semilinear parabolic equation governed by bilinear control, ESAIM: Contrôle, Optimisation et Calcul des Variations, 7, ( 2002), pp 269-283.

9. Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach, SIAM. J. Contr. Opt. 41 (2003), 1886-1900.

10. Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation, In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, December 10-13, 2002, 6p.

11. Bilinear controllability properties of a vibrating string with variable axial load and damping gain, Dynamics of Continuous, Discrete and Impulsive Systems, 10 (2003), 721-743. 27.

12. Energy Decay Estimates for Lienard's equation with Quadratic Viscous Feedback, (with P. Nag) Electr J. Diff. Eqs., 2003, pp 1-12.

13. Controllability properties of a vibrating string with variable axial load, Discrete and Continuous Dynamical Systems, 11 (2004), pp. 311-324.

14. Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach, Proc. of the 42nd IEEE Conference on Decision and Control (CDC 2003), December 9-12, 2003, in Maui, Hawaii, 6 p.

15. Progress in partial differential equations. Papers from the Conference on Partial Differential Equations held at Washington State University, Pullman, WA May 23 - 25 ,2003 in honor of the 65th birthday of John R. Cannon. Edited by R. Dillon, A. Khapalov, V.S. Manoranjan and H. M. Yin. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal 10 (2003), no. 5, Watam Press, Waterloo, ON pp. i - iv and 635, 861.

16. Controllability properties of a vibrating string with variable axial load, Discrete and Continuous Dynamical Systems 11 (2004), pp. 311-324.

17. Non-negative reachability for the semilinear wave equation by means of two multiplicative controls, ESAIM: Contrôle, Optimisation et Calcul des Variations, (In press).

18. Energy decay estimate for a power system model using FACTS stabilizer (with P. Nag), Dyn. Contin. Discrete Impuls. Syst. Ser. A., (In press).