%0 Journal Article %1 harris1999travellingwaves %A Harris, Simon C. %D 1999 %J Proc. Roy. Soc. Edinburgh Sect. A %K Fisher-KPP branching_Brownian_motion travelling_wave %N 3 %P 503--517 %R 10.1017/S030821050002148X %T Travelling-waves for the FKPP equation via probabilistic arguments %U http://dx.doi.org/10.1017/S030821050002148X %V 129 %X We outline a completely probabilistic study of travelling-wave solutions of the FKPP reaction-diffusion equation that are monotone and connect 0 to 1. The necessary asymptotics of such travelling-waves are proved using martingale and Brownian motion techniques. Recalling the connection between the FKPP equation and branching Brownian motion through the work of McKean and Neveu, we show how the necessary asymptotics and results about branching Brownian motion combine to give the existence and uniqueness of travelling waves of all speeds greater than or equal to the critical speed.

@article{harris1999travellingwaves, abstract = {We outline a completely probabilistic study of travelling-wave solutions of the FKPP reaction-diffusion equation that are monotone and connect 0 to 1. The necessary asymptotics of such travelling-waves are proved using martingale and Brownian motion techniques. Recalling the connection between the FKPP equation and branching Brownian motion through the work of McKean and Neveu, we show how the necessary asymptotics and results about branching Brownian motion combine to give the existence and uniqueness of travelling waves of all speeds greater than or equal to the critical speed. }, added-at = {2013-09-12T21:04:59.000+0200}, author = {Harris, Simon C.}, biburl = {https://www.bibsonomy.org/bibtex/25c15bd77165e65c15b693fa4a6147b5b/peter.ralph}, coden = {PEAMDU}, description = {MR: Publications results for "MR Number=(1693633)"}, doi = {10.1017/S030821050002148X}, fjournal = {Proceedings of the Royal Society of Edinburgh. Section A. Mathematics}, interhash = {85ecdc24b4dc8d3574e94c422958b52a}, intrahash = {5c15bd77165e65c15b693fa4a6147b5b}, issn = {0308-2105}, journal = {Proc. Roy. Soc. Edinburgh Sect. A}, keywords = {Fisher-KPP branching_Brownian_motion travelling_wave}, mrclass = {35K57 (60G44 60J60 60J80)}, mrnumber = {1693633 (2000g:35109)}, mrreviewer = {Ying Guo Lei}, number = 3, pages = {503--517}, timestamp = {2013-09-12T21:04:59.000+0200}, title = {Travelling-waves for the {FKPP} equation via probabilistic arguments}, url = {http://dx.doi.org/10.1017/S030821050002148X}, volume = 129, year = 1999 }