Abstract and Applied Analysis

Robustness of Exponential Dissipation with respect to Small Time Delay

Xunwu Yin

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511921

Digital Object Identifier
doi:10.1155/2013/361970

Mathematical Reviews number (MathSciNet)
MR3064539

Zentralblatt MATH identifier
1291.93240

Citation

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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