JOURNAL BROWSE
Search
Advanced SearchSearch Tips
PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES
Kang, Yong Han; Jeong, Jin-Mun;
  PDF(new window)
 Abstract
The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.
 Keywords
perturbation theory;hyperbolic equations;fundamental solution;regularity;analytic semigroup;
 Language
English
 Cited by
 References
1.
A. Belarbi and M. Benchohra, Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times, J. Math. Anal. Appl. 327 (2007), no. 2, 1116-1129. crossref(new window)

2.
W. S. Edelstein and M. E. Gurtin, Uniqueness theorem in the linear dynamic theory of anisotropic viscoelastic solid, Arch. Rat. Mech. Anal. 17 (1964), 47-60.

3.
M. J. Garrido-Atienza and J. Real, Existence and uniqueness of solutions for delay evolution equations of second order in time, J. Math. Anal. Appl. 283 (2003), no. 2, 582-609. crossref(new window)

4.
J. A. Goldstein, Semigroup of Linear Operators and Applications, Oxford University Press, Inc. 1985.

5.
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. crossref(new window)

6.
A. G. Kartsatos and L. P. Markov, An $L_2$-approach to second-order nonlinear functional evolutions involving m-accretive operators in Banach spaces, Differential Integral Equations 14 (2001), no. 7, 833-866.

7.
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966.

8.
T. Kato, Linear evolutions equations of "hyperbolic" type, J. Fac. Sci. Uni. Tokyo Sec. I 17 (1970), 241-258.

9.
J. L. Lions and E. Magenes, Non-Homogeneous Boundary value Problems and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 1972.

10.
D. G. Park, J. M. Jeong, and H. G. Kim, Regular problems for semilinear hyperbolic type equations, Nonlinear Differ. Equ. Appl. 16 (2009), 235-253. crossref(new window)

11.
R. S. Phillips, Perturbation theory for semi-groups of linear operator, Trans. Amer. Math. Soc. 74 (1953), 199-221. crossref(new window)

12.
H. Tanabe, Equations of Evolution, Pitman-London, 1979.

13.
J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer- Verlag, Newyork, 1996.

14.
K. Yosida, Functional Analysis, 2nd ed, Springer-Verlag, Berlin, Heidelberg, New York, 1968.