On exact rates of decay of solutions of linear systems of Volterra equations with delay |
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Authors: | John AD Appleby David W Reynolds |
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Institution: | a School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland b Department of Mathematics and Computing, University of Veszprém, Veszprém, Hungary |
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Abstract: | This paper considers the resolvent of a finite-dimensional linear convolution Volterra integral equation. The main results give conditions which ensure that the exact rate of decay of the resolvent can be determined using a positive weight function related to the kernel. The decay rates can be exponential or subexponential. Many other related results on exact rates of exponential and subexponential decay of solutions of Volterra integro-differential equations are given. We also present an application to a linear compartmental system with discrete and continuous lags. |
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Keywords: | Volterra integral equations Volterra integro-differential equations Asymptotic behaviour Subexponential functions Subexponential distributions Characteristic equations |
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