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On the Role of Diffusion Behaviors in Stability Criterion for p‐Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value

Author

Listed:
  • Ruofeng Rao
  • Zhilin Pu
  • Shouming Zhong
  • Jialin Huang

Abstract

By the way of Lyapunov‐Krasovskii functional approach and some variational methods in the Sobolev space W01,p(Ω), a global asymptotical stability criterion for p‐Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p‐Laplace diffusion item plays its role in the new criterion though the nonlinear p‐Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.

Suggested Citation

  • Ruofeng Rao & Zhilin Pu & Shouming Zhong & Jialin Huang, 2013. "On the Role of Diffusion Behaviors in Stability Criterion for p‐Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:940845
    DOI: 10.1155/2013/940845
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    References listed on IDEAS

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    1. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2012. "LMI Approach to Stability Analysis of Cohen‐Grossberg Neural Networks with p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Yutian Zhang, 2012. "Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, November.
    3. Xiao Liang & Linshan Wang, 2012. "Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, March.
    4. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian‐Jumping Cohen‐Grossberg Neural Networks with Nonlinear p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear -Laplace Diffusion," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-21, May.
    6. Abdelmalek Salem, 2007. "Invariant Regions and Global Existence of Solutions for Reaction‐Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2007(1).
    7. Abdelmalek Salem, 2007. "Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions," Journal of Applied Mathematics, Hindawi, vol. 2007, pages 1-15, December.
    8. Yutian Zhang, 2012. "Asymptotic Stability of Impulsive Reaction‐Diffusion Cellular Neural Networks with Time‐Varying Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    9. Xiao Liang & Linshan Wang, 2012. "Exponential Stability for a Class of Stochastic Reaction‐Diffusion Hopfield Neural Networks with Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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