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Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time‐Delayed Degenerate Diffusion Equation

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  • Weifang Yan
  • Rui Liu

Abstract

This paper is concerned with traveling wave fronts for a degenerate diffusion equation with time delay. We first establish the necessary and sufficient conditions to the existence of monotone increasing and decreasing traveling wave fronts, respectively. Moreover, special attention is paid to the asymptotic behavior of traveling wave fronts connecting two uniform steady states. Some previous results are extended.

Suggested Citation

  • Weifang Yan & Rui Liu, 2013. "Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time‐Delayed Degenerate Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:578345
    DOI: 10.1155/2013/578345
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    References listed on IDEAS

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    1. Na Min & Hongyang Zhang & Zhilin Qu, 2012. "Dynamic Properties of a Forest Fire Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    4. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, October.
    5. Na Min & Hongyang Zhang & Zhilin Qu, 2012. "Dynamic Properties of a Forest Fire Model," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
    6. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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