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Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay

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  • Yueding Yuan
  • Zhiming Guo

Abstract

We study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. By using a fluctuation method, combined with the careful analysis of the corresponding characteristic equations, we obtain some sufficient conditions for the global asymptotic stability of the trivial solution and the positive steady state to the equations subject to the Neumann boundary condition.

Suggested Citation

  • Yueding Yuan & Zhiming Guo, 2014. "Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jnlaaa:378172
    DOI: 10.1155/2014/378172
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