DOI QR코드

DOI QR Code

REGULARITY FOR SEMILINEAR RETARDED FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

Jeong, Jin-Mun;Cheon, Su Jin

  • Received : 2012.09.26
  • Published : 2013.07.31

Abstract

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

Keywords

semilinear equation;retarded functional integrodifferential equation;existence of solution;uniqueness of solution;norm estimation

References

  1. J. P. Aubin, Un theoreme de compacite, C. R. Acad. Sci. Paris 256 (1963), 5042-5044.
  2. G. Di Blasio, K. Kunisch, and E. Sinestrari, $L^2$-regularity for parabolic partial integrodif-ferential equations with delay in the highest-order derivatives, J. Math. Anal. Appl. 102 (1984), no. 1, 38-57. https://doi.org/10.1016/0022-247X(84)90200-2
  3. W. E. Fitzgibbon, Semilinear integro-differential equations in Banach space, Nonlinear Anal. 4 (1980), no. 4, 745-760. https://doi.org/10.1016/0362-546X(80)90075-9
  4. M. L. Heard, An abstract semilinear hyperbolic Volterra integro-differential equation, J. Math. Anal. Appl. 80 (1981), no. 1, 175-202. https://doi.org/10.1016/0022-247X(81)90101-3
  5. J. M. Jeong, S. Nakagiri, and H. Tanabe, Structural operators anf semigroups associated with functional-differential equations in Hilbert space, Osaka J. Math. 30 (1993), no. 3, 365-395.
  6. J. M. Jeong, Retarded functional-differential equations with $L^1$-valued controller, Funkcial. Ekvac. 36 (1993), no. 1, 71-93.
  7. H. Tanabe, Fundamental solutions of differential equation with time delay in Banach space, Funkcial. Ekvac. 35 (1992), no. 1, 149-177.
  8. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978.
  9. J. Yong and L. Pan, Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives, J. Austral. Math. Soc. Ser. A 54 (1993), no. 2, 174-203. https://doi.org/10.1017/S1446788700037101

Acknowledgement

Supported by : National research Foundation of Korea(NRF