Stability conditions for abstract functional differential equations in Hilbert space

Abstract

Stability conditions for functional differential equations of the form: du (t)/dt = Au(t) + bAu(t-h) + (a*Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b ǂ 0 and the convolution term contains a square integrable real function a ǂ 0. Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup are obtained. The results are applied to a retarded partial integrodifferential equation.

Keywords

enačbe;diferencialne enačbe;diferencialni račun;

Data

Language:	English
Year of publishing:	2003
Typology:	1.01 - Original Scientific Article
Organization:	UM EPF - Faculty of Economics and Business
UDC:	330.4
COBISS:	6521884
ISSN:	0037-1912
Views:	864
Downloads:	95
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	enačbe;diferencialne enačbe;diferencialni račun;
URN:	URN:SI:UM:
Pages:	str. 140-150
Issue:	ǂVol. ǂ66
Chronology:	2003
ID:	8719974