## Abstract and Applied Analysis

### Robustness of Exponential Dissipation with respect to Small Time Delay

Xunwu Yin

#### Abstract

We investigate robustness of exponential dissipation for the following general nonlinear evolutionary equation with small time delay: ${\partial }_{t}u+Au=f\left(u\left(t\right),u\left(t-\tau \right)\right).$ 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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