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Multidimensional transition fronts for Fisher-KPP reactions

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 نشر من قبل Jessica Lin
 تاريخ النشر 2016
  مجال البحث
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We study entire solutions to homogeneous reaction-diffusion equations in several dimensions with Fisher-KPP reactions. Any entire solution $0<u<1$ is known to satisfy [ lim_{tto -infty} sup_{|x|le c|t|} u(t,x) = 0 qquad text{for each $c<2sqrt{f(0)},$,} ] and we consider here those satisfying [ lim_{tto -infty} sup_{|x|le c|t|} u(t,x) = 0 qquad text{for some $c>2sqrt{f(0)},$.} ] When $f$ is $C^2$ and concave, our main result provides an almost complete characterization of transition fronts as well as transition solutions with bounded width within this class of solutions.



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