Exponential decay of a first order linear Volterra equation
We consider the linear Volterra equation of the first order in time $$\dot u(t)+\int_0^t g(s)A u(t-s) d s=0$$ where $A$ is a positive bounded operator on a Hilbert space $H$. The exponential decay of the related energy is shown to occur, provided that the kernel $g$ is controlled by a negative expon...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-05-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020021/fulltext.html |