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On exponential stability criteria of stochastic partial differential equations

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  • Caraballo, Tomás
  • Liu, Kai

Abstract

Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential equations are shown in this paper. In particular, the main results obtained in Caraballo and Real (1994, Stochast. Anal. Appl. 12(5), 517-525) are improved, since the new coercivity condition introduced in this work permits the state independent term [gamma] to be time dependent and nonnegative but of subexponential growth, while in Caraballo and Real (1994) this parameter is required to be constant and nonpositive. Several examples are studied to illustrate the theory.

Suggested Citation

  • Caraballo, Tomás & Liu, Kai, 1999. "On exponential stability criteria of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 289-301, October.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:2:p:289-301
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    Cited by:

    1. Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
    2. Y. Ren & D. D. Sun, 2010. "Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 569-582, December.
    3. Wan, Li & Duan, Jinqiao, 2008. "Exponential stability of non-autonomous stochastic partial differential equations with finite memory," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 490-498, April.

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