# OPTIMAL PROBLEM FOR RETARDED SEMILINEAR DIFFERENTIAL EQUATIONS

• Park, Dong-Gun (Department of Mathematics Long-A University) ;
• Jeong, Jin-Mun (Division of Mathematical sciences Pukyong National University) ;
• Kang, Weon-Kee (Department of Mathematics Long-A University)
• Published : 1999.03.01
• 40 5

#### Abstract

In this paper we deal with the optimal control problem for the semilinear functional differential equations with unbounded delays. We will also establish the regularity for solutions of the given system. By using the penalty function method we derive the optimal conditions for optimality of an admissible state-control pairs.

#### Keywords

retarded semilinear differential equations;optimal pairs;penalty function;optimal conditions

#### References

1. Funkcial. Ekvac. v.35 Fundamental solutions of differential equation with time delay in Banach space H. Tanabe
2. J. Functional Anal. v.17 On the existence of Von Neuman-Aumann's Theorem M. F. Saint-Beuve
3. SIAM J. Control and Optimization v.6 Boundary control systems H. O. Fattorini
4. Funckcial. Ekvac. v.36 Retarded functional differential equations with $L^1$ -valued controller J. M. Jeong
5. J. Indust. Appl. Math. v.10 Infinite dimensional parametric optimal control problems N. S. Papageorgiou
6. Indian J. Pure and Applied Math. Regularity and controllability for semilinear control system J. Y. Park;J. M. Jeong;Y. C. Kwun
7. Japan J. Indust. Appl. Math v.10 Infinite dimensional parametric optimal control problems S. Aizicovici;N. S. Papageorgiou
8. J. Math. Anal. Appl. v.102 $L^2$-regularity for parabolic partial intergrodifferential equations with delay in the highest-order derivatives G. Di Blasio;K. Kunisch;E. Sinestrari
9. J. Math. Anal. Appl. v.164 On the optimal control of strongly nonlinear evolution equations N. S. Papageorgiou
10. C. R. Acad. Sci. v.256 Un theoreme de compasite J. P. Aubin