Periodic pyramidal traveling fronts of bistable reaction-diffusion equations with time-periodic nonlinearity

By Weijie Sheng, Wan-Tong Li, Zhi-Cheng Wang. 2012

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Abstract This paper deals with the existence and stability of periodic pyramidal traveling fronts for reaction–diffusion equations with bistable time-periodic nonlinearity in R N with N ⩾ 3 . It is well known that two-dimensional periodic traveling curved fronts exist and are stable. In this paper, by constructing various of supersolutions and subsolutions, we first show that there exist three-dimensional periodic pyramidal traveling fronts, and then we prove that such periodic pyramidal traveling fronts are asymptotically stable. Finally, we further prove that our existence result holds for R N with N ⩾ 4 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Public Health, Environmental and Occupational Health

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