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The Approach of Solutions for the NonlocalDiffusion Equation to Traveling Fronts
  
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KeyWord:Entire solution  Traveling front  Nonlocal evolution equation  Super-sub
Author NameAffiliation
Shaohua Gan College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 
Zhixian Yu Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 
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Abstract:
      The paper is concerned with the asymptotic behavior as t → ±∞ of an entire solution u(x,t) for the nonlocal diffusion equation. With bistable assumption, it is well known that the model has three different types of travel- ing fronts. Under certain conditions on the wave speeds, and by some auxiliary rational functions with certain properties to construct appropriate super- and sub solutions of the model, we establish two new types of entire solutions u(x,t) which approach to three travelling fronts or the positive equilibrium as t → ±∞.