%0 Journal Article %1 françois2001travelling %A Hamel, François %A Nadirashvili, Nikolaï %D 2001 %J Archive for Rational Mechanics and Analysis %K Fisher-KPP travelling_wave %N 2 %P 91--163 %T Travelling Fronts and Entire Solutions of the Fisher-KPP Equation in $\R^N$ %U http://dx.doi.org/10.1007/PL00004238 %V 157 %X 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.

@article{françois2001travelling, abstract = {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. }, added-at = {2010-01-18T19:07:48.000+0100}, author = {Hamel, François and Nadirashvili, Nikolaï}, biburl = {https://www.bibsonomy.org/bibtex/2c0ff43688abcbb24ba549b1d0ce880d7/peter.ralph}, description = {Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN}, interhash = {10230b62fc8cb5fa748cdcba64fa9207}, intrahash = {c0ff43688abcbb24ba549b1d0ce880d7}, journal = {Archive for Rational Mechanics and Analysis}, keywords = {Fisher-KPP travelling_wave}, month = {#apr#}, number = 2, pages = {91--163}, timestamp = {2013-09-12T22:23:01.000+0200}, title = {Travelling Fronts and Entire Solutions of the Fisher-KPP Equation in $\R^N$}, url = {http://dx.doi.org/10.1007/PL00004238}, volume = 157, year = 2001 }