×

zbMATH — the first resource for mathematics

Asymptotic stability for a class of integrodifferential equations. (English) Zbl 0668.45012
The asymptotic stability of a class of abstract semi-linear Volterra equations, involving infinite delay, is studied. Relevant theorems and lemmas are proved, and a final practical example is given.
Reviewer: V.Boffi

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45M05 Asymptotics of solutions to integral equations
45M10 Stability theory for integral equations
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] J. Finn, L. Wheeler: Wave propagation aspects of the generalized theory of heat conduction. Z. Angew. Math. Physics, 23 (1972), 927-940. · Zbl 0249.35034
[2] W. Fitzgibbon: Abstract hyperbolic integrodifferential equations. J. Math, Anal. Appl., 84(1981),299-310. · Zbl 0506.45016
[3] W. Fitzgibbon: Convergence theorem for semilinear Volterra equations with infinite delay. J. Integral Equations · Zbl 0569.45019
[4] W. Fitzgibbon: Nonlinear Volterra equations with infinite delay. Monat Math, 84 (1977), 275-288. · Zbl 0382.45003
[5] W. Fitzgibbon: Semilinear integrodifferential equations in Banach space. J. Nonlinear Analysis: TMA, 4 (1980), 745-760. · Zbl 0442.45014
[6] A. Friedman: Partial Differential Equations. Holt, Rhinehart and Winston, New York, 1969. · Zbl 0224.35002
[7] J. Goldstein: Semigroups of Operators and Abstract Cauchy Problems. Lecture Notes, Tulane University, 1970. · Zbl 0219.47037
[8] T. Kato: Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, 1966. · Zbl 0148.12601
[9] M. Heard: An abstract semilinear hyperbolic Volterra integrodifferential equations. Integral and Functional Differential Equations, Lecture notes in Pure and Applied Mathematics, 67, Marcel Dekker, 1979, New York, 185-193.
[10] R. MacCamy: An integrodifferential equation with applications in heat flow. Q. Appl. Math. 35 (1977), 1-9. · Zbl 0351.45018
[11] J. Nunziato: On heat conduction in materials with memory. Q. Appl. Math. 29 (1971) 187-204. · Zbl 0227.73011
[12] J. Nohel: Nonlinear Volterra equations for heat flow in materials with memory. Integral and Functional Differential Equations, Lecture Notes in Pure and Applied Mathematics 67, Marcel Dekker, 1979, New York, 3 - 82.
[13] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin, 1983. · Zbl 0516.47023
[14] R. Redlinger: On the asymptotic stability of a semilinear functional differential equation in Banach space. J. Math. Anal. Appl. · Zbl 0598.34053
[15] C. Travis, G. Webb: An abstract second order semilinear Volterra integrodifferential equations. SIAM J. Math. Anal. 10 (1979), 412-424. · Zbl 0406.45014
[16] G. Webb: An abstract semilinear Volterra integrodifferential equation. Proc. Amer. Math. Soc.,69 (1978), 255-260. · Zbl 0388.45012
[17] G. Webb: A class of reaction-diffusion equations. Proc. Intl. Conf. on Volterra Equations, Helsinki, Lecture Notes in Mathematics, Springer-Verlag, Berlin 1982.
[18] G. Webb: Volterra integral equations and nonlinear semigroups. J. Nonlinear Analysis: TMA, 1 (1977), 415-427. · Zbl 0364.45007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.