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Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN

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This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝN:

where f is a C 2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.

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Accepted October 30, 2000¶Published online March 21, 2001

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Hamel, F., Nadirashvili, N. Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN. Arch. Rational Mech. Anal. 157, 91–163 (2001).

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