caa a22 4500 386382794 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500024057 doi S0308210500024057 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500024057 Blow up for a diffusion-advection equation [Elektronische Daten] These results describe the asymptotic behaviour of solutions to a certain non-linear diffusionadvection equation on the unit interval. The "no flux” boundary conditions prescribed result in mass being conserved by solutions and the existence of a mass-parametrised family of equilibria. A natural question is whether or not solutions stabilise to equilibria and if not, whether they blow up in finite time. Here it is shown that for non-linearities which characterise "fast association” there is a criticalmass such that initial data which have supercritical mass must lead to blow up in finite time. It is also shown that there exist initial data with arbitrarily small mass which also lead to blow up in finite time. Copyright © Royal Society of Edinburgh 1989 Alikakos Nicholas D. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A Bates Peter W. Applied Mathematics, National Science Foundation, Washington, D.C. 20550, U.S.A Grant Christopher P. Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 181-190 0308-2105 113:3-4<181 1989 113 PRM https://doi.org/10.1017/S0308210500024057 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500024057 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alikakos Nicholas D. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A NATIONALLICENCE 700 1- Bates Peter W. Applied Mathematics, National Science Foundation, Washington, D.C. 20550, U.S.A NATIONALLICENCE 700 1- Grant Christopher P. Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 181-190 0308-2105 113:3-4<181 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge