Abstract and Applied Analysis

Robustness of Exponential Dissipation with respect to Small Time Delay

Xunwu Yin

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We investigate robustness of exponential dissipation for the following general nonlinear evolutionary equation with small time delay: t u + A u = f ( u ( t ) , u ( t τ ) ). We firstly obtain a converse Lyapunov theorem. With the help of it, we establish an important result on robustness of exponential dissipation to small time delay assuming that the nonlinearity is globally Lipschitz.

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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 361970, 8 pages.

First available in Project Euclid: 27 February 2014

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Yin, Xunwu. Robustness of Exponential Dissipation with respect to Small Time Delay. Abstr. Appl. Anal. 2013 (2013), Article ID 361970, 8 pages. doi:10.1155/2013/361970. https://projecteuclid.org/euclid.aaa/1393511921

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