Acta mathematica scientia, Series B >
EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS
Received date: 2012-01-17
Online published: 2013-05-20
Supported by
This work is supported by NSF of China (11171110) and Shanghai Leading Academic Discipline Project (B407).
In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condi-tion or Lipschitz condition for the function g in the nonlocal conditions appearing in various
literatures is not required here. An example is also provided to show an application of the obtained result.
FU Xian-Long , ZHANG Yu . EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 747 -757 . DOI: 10.1016/S0252-9602(13)60035-1
[1] Dauer J P, Balasubramaniam P. Null controllability of semilinear integrodifferential systems in Banach spaces. App Math Lett, 1997, 10: 117–123
[2] Balachandran K, Balasubramaniam P, Dauer J P. Local null controllability of nonilinear functional differ-ential systems in Banach spaces. J Optim Theory Appl, 1996, 88: 61–75
[3] Dauer J P, Mahmudov N I. Exact null controllability of semilinear integrodifferential systems in Hilbert spaces. J Math Anal Appl, 2004, 299: 322–332
[4] Byszewski L. Theorems about existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem. J Math Anal Appl, 1991, 162: 496–505
[5] Deng K. Exponential decay of solutions of semiliear parabolic equations with nonlocal initial conditions. J Math Anal Appl, 1993, 179: 630–637
[6] Ezzinbi K, Fu X, Hilal K. Existence and regularity in the -norm for some neutral partial differential equations with nonlocal conditions. Nonl Anal, 2007, 67: 1613–1622
[7] Fu X. Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions. J Dyn Contr Syst, 2011, 17: 359–386
[8] Fu X, Liu X. Existence of solutions for neutral non-autonomous evolution equations with nonlocal condi-tions. Indian J Pure Appl Math, 2006, 37: 179–192
[9] Guo M, Xue X, Li R. Controllability of impulsive evolution inclusions with nonlocal conditions. J Optim Theory Appl, 2004, 120: 355–374
[10] Liang J, Liu J H, Xiao T. Nonlocal cauchy problems governed by compact operator families. Nonlinear Anal, 2004, 57: 183–189
[11] Mahmudov N I. Approximate controllability of evolution systems with nonlocal conditions. Nonl Anal, 2008, 68: 536–546
[12] Fitzgibbon W E. Semilinear functional equations in Banach space. J Diff Equ, 1978, 29: 1–14
[13] Rankin III S M. Existence and asymptotic behavior of a functional differential equation in Banach space. J Math Anal Appl, 1982, 88: 531–542
[14] Friedman A. Partial Differential Equations. New York: Holt, Rinehat and Winston, 1969
[15] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York: Springer-Verlag, 1983
[16] Curtain R, Zwart H J. An Introduction to Infinite Dimensional Linear Systems Theory. New York: Springer-Verlag, 1995
/
| 〈 |
|
〉 |