LI Panxiao. Exponential Stability of Traveling Wavefronts for ReactionDiffusion Equations With Delayed Nonlocal Responses[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1300-1312. doi: 10.21656/1000-0887.380336
Citation: LI Panxiao. Exponential Stability of Traveling Wavefronts for ReactionDiffusion Equations With Delayed Nonlocal Responses[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1300-1312. doi: 10.21656/1000-0887.380336

Exponential Stability of Traveling Wavefronts for ReactionDiffusion Equations With Delayed Nonlocal Responses

doi: 10.21656/1000-0887.380336
Funds:  The National Natural Science Foundation of China(11671315)
  • Received Date: 2017-12-28
  • Rev Recd Date: 2018-02-02
  • Publish Date: 2018-11-01
  • A spatially nonlocal diffusion model with a class of delayed nonlocal responses was considered. The asymptotic stability and the convergence rate of the traveling wavefronts were mainly studied. Through construction of weighted functions and establishment of a comparison principle for the related linear equations, the conclusion that if the initial function is within a bounded distance from a certain traveling wavefront with respect to a weighted maximum norm, the solution satisfying the initial value will converge to the traveling wavefront exponentially in time, was proved, and the exponential convergence rate was also obtained.
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