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Uniform exponential stability of solutions to abstract Volterra equations

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Abstract

In terms of the spectral properties of the associated operator matrix, we obtain a new criterion to judge the uniform exponential stability of the solutions to abstract Volterra equations. In particular, we study in detail the case where the kernel function a(t) takes the form α e −βt (β > 0, α ≠ 0). Moreover, we give examples to illustrate our results.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Jian-Hua Chen

  2. School of Mathematical Sciences, Fudan University, 200433, Shanghai, People’s Republic of China

    Ti-Jun Xiao

  3. Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, People’s Republic of China

    Jin Liang

Authors
  1. Jian-Hua Chen
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  2. Ti-Jun Xiao
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  3. Jin Liang
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Corresponding author

Correspondence to Ti-Jun Xiao.

Additional information

The work was supported partly by the NSF of China (10771202), the Research Fund for Shanghai Key Laboratory of Modern Applied Mathematics (08DZ2271900) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007035805).

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Chen, JH., Xiao, TJ. & Liang, J. Uniform exponential stability of solutions to abstract Volterra equations. J. Evol. Equ. 9, 661 (2009). https://doi.org/10.1007/s00028-009-0028-4

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  • DOI: https://doi.org/10.1007/s00028-009-0028-4

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