caa a22 4500 388109017 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S030821050002148X doi S030821050002148X pii (NATIONALLICENCE)cambridge-10.1017/S030821050002148X Harris Simon C. Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK Travelling-waves for the FKPP equation via probabilistic arguments [Elektronische Daten] [Simon C. Harris] 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. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/3(1999), 503-517 0308-2105 129:3<503 1999 129 PRM https://doi.org/10.1017/S030821050002148X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030821050002148X text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Harris Simon C. Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/3(1999), 503-517 0308-2105 129:3<503 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge