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p th Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations

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  • Xuetao Yang
  • Quanxin Zhu
  • Zhangsong Yao

Abstract

We are concerned with the exponential stability problem of a class of nonlinear hybrid stochastic heat equations (known as stochastic heat equations with Markovian switching) in an infinite state space. The fixed point theory is utilized to discuss the existence, uniqueness, and th moment exponential stability of the mild solution. Moreover, we also acquire the Lyapunov exponents by combining the fixed point theory and the Gronwall inequality. At last, two examples are provided to verify the effectiveness of our obtained results.

Suggested Citation

  • Xuetao Yang & Quanxin Zhu & Zhangsong Yao, 2014. "p th Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, August.
    • Handle: RePEc:hin:jnlmpe:481246
    DOI: 10.1155/2014/481246
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    Cited by:

    1. Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.

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