Approximate controllability of the impulsive semilinear heat equation

Abstract (pdf)

Full text (pdf)

1. J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, 60. Marcel Dekker, Inc., New York, 1980.
2. D.Barcenas, H. Leiva and Z. Sivoli, A Broad Class of Evolution Equations are Approximately Controllable, but Never Exactly Controllable. IMA J. Math. Control Inform. 22,  no. 3  (2005), 310-320.
3. H. Brezis, Analisis Funcional, Teoria  Applicaciones. Alianza Universitaria Textos, Masson, Paris, 1983. Ed. cast.: Alinza Editorial, S. A., Madrid, 1984.
4. D. N. Chalishajar, Controllability of Impulsive Partial Neutral Funcional Differential Equation with Infinite Delay. Int. Journal of Math. Analysis, Vol. 5, 2011, Nº. 8, 369-380.
5. Lizhen Chen and Gang Li, Approximate Controllability of Impulsive  Differential Equations with Nonlocal Conditions. International Journal of Nonlinear Science, Vol.10(2010), Nº. 4, pp. 438-446.
6. R.F. Curtain and A.J. Pritchard, Infinite Dimensional Linear Systems. Lecture Notes in Control and Information Sciences, 8. Springer Verlag, Berlin (1978).
7. R.F. Curtain, H.J. Zwart,  An Introduction to Infinite Dimensional Linear Systems Theory. Text in Applied Mathematics, 21. Springer Verlag, New York (1995).
8. Lawrence C. Evans, Partial Differential Equations. Graduate Studies in Mathematics, Vol. 19, AMS. 1999.
9. G. Isac, On Rothe's Fixed Point Theorem in General Topological Vector Space,  An. St. Univ. Ovidius Constanta, Vol. 12(2), 2004, 127-134.
10. C. Kesavan, Topics in: Functional Analysis and Applications. John Wiley and Sons, 1989.
11. H. Leiva``Controllability of a System of Parabolic equation with non-diagonal diffusion matrix''. IMA Journal of Mathematical Control and Information; Vol. 32, 2005, pp. 187-199.
12. H. Leiva and Y. Quintana, Interior Controllability of a Broad Class of Reaction Diffusion Equations',  Mathematical Problems in Engineering, Vol. 2009, Article ID 708516, 8 pages, doi:10.1155/2009/708516.
13. H. Leiva, N. Merentes and J.L. Sanchez, Interior Controllability of the nD Semilinear Heat Equation''. African Diaspora Journal of Mathematics, Special Vol. in Honor of Profs. C. Corduneanu, A. Fink, and S. Zaidman. Vol. 12, Nº. 2, pp. 1-12(2011).
14. H. Leiva, N. Merentes and J. Sanchez "Approximate Controllability of Semilinear Reaction Diffusion" MATHEMATICAL CONTROL AND RALATED FIELDS, Vol. 2,Nº.2, June 2012.
15. H. Leiva, N. Merentes and J. Sanchez "A Characterization of Semilinear  Dense Range Operators and Applications", Abstract and Applied Analysis, Vol. 2013, Article ID 729093, 11 pages.
16. H. Leiva, N. Merentes and J.L. Sanchez ``Interior Controllability of the Benjamin-Bona-Mahony Equation''. Journal of Mathematis and Applications, Nº 33,pp. 51-59 (2010).
17. A. Pazy,  Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, (1983).
18. M.H. Protter, Unique continuation for elliptic equations. Transaction of the American Mathematical Society, Vol. 95, Nº 1, Apr., 1960.
19. B. Radhakrishnan and  K. Blachandran, Controllability Results for Semilinear Impulsive Integrodifferential Evolution Systems with Nonlocal Conditions, J. Control Theory Appl. 2012, 10(1), 28-34.
20. S. Selvi and M. Mallika Arjunan, Controllability Results for Impulsive Differential Systems with Finite Delay J. Nonlinear Sci. Appl. 5 (2012), 206-219.
21. J. D.R. Smart, Fixed Point Theorems, Cambridge University Press (1974).
22. Xu Zhang,  A Remark on Null Exact Controllability of the Heat Equation. IAM J. CONTROL OPTIM. Vol. 40, No. 1(2001), pp. 39-53.
23. E. Zuazua, Controllability of a System of Linear Thermoelasticity, J. Math. Pures Appl., 74, (1995), 291-315.
24. E. Zuazua, Control of Partial Differential Equations and its Semi-Discrete Approximation. Discrete and Continuous Dynamical Systems, vol. 8, No. 2. April (2002), 469-513.