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Dynamic behavior of a heat equation with memory

โœ Scribed by Jun-Min Wang; Bao-Zhu Guo; Meng-Yin Fu

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
177 KB
Volume
32
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Abstract

This paper addresses the spectrumโ€determined growth condition for a heat equation with exponential polynomial kernel memory. By introducing some new variables, the timeโ€variant system is transformed into a timeโ€invariant one. The detailed spectral analysis is presented. It is shown that the system demonstrates the property of hyperbolic equation that all eigenvalues approach a line that is parallel to the imaginary axis. The residual spectral set is shown to be empty and the set of continuous spectrum is exactly characterized. The main result is the spectrumโ€determined growth condition that is one of the most difficult problems for infiniteโ€dimensional systems. Consequently, a strong exponential stability result is concluded. Copyright ยฉ 2008 John Wiley & Sons, Ltd.

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