Abstract
In this paper, we establish the well-posedness of solutions and regularity properties for the boundary control systems with nonlocal conditions with the aid of an intermediate property and the contraction mapping principle. A numerical example illustrating our equivalence results is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. P. Aubin, Un thèoréme de compacité. C. R. Acad. Sci. 279 (1963), 5042–5044.
G. Di Blasio, K. Kunisch, and E. Sinestrari, L 2-Regularity for parabolic partial integrodifferential equations with delay in the highest-order derivatives. J. Math. Anal. Appl. 102 (1984), 38–57.
V. Barbu and T. Precupanu, Convexity and optimization in Banach spaces. Reidel, New York (1986).
L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991), 494–505.
H. Han and J. Park, Boundary controllability of differential equations with nonlocal condition. J. Math. Anal. Appl. 230 (1999), 242–250.
D. Jackson, Existence and uniqueness of solutions to semilinear nonlocal parabolic equations. J. Math. Anal. Appl. 172 (1993), 256–265.
J. M. Jeong, Y. C. Kwun, and J. Y. Park, Approximate controllability for semilinear retarded functional differential equations. J. Dynam. Control Systems 5 (1999), No. 3, 329–346.
M. A. Krasnoselski, Topological methods in the theory of nonlinear integral equations. Pergamon Press, New York (1964).
J. L. Lions and E. Magenes, Non-homogeneous boundary-value problems and applications. Vol. 1. Springer-Verlag, Berlin (1972).
K. Naito, Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25 (1987), 715–722.
R. Triggiani, A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J. Control Optim. 15 (1977), 407–411.
D. Washburn, A bound on the boundary input map for parabolic equations with application to time optimal control. SIAM J. Control Optim. 17 (1979), 652–671.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Park, DG., Jeong, JM. & Kim, HG. Regularity for semilinear nonlocal problems with boundary input maps. J Dyn Control Syst 15, 247–261 (2009). https://doi.org/10.1007/s10883-009-9062-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10883-009-9062-3