caa a22 4500 386382808 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500024185 doi S0308210500024185 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500024185 The asymptotic behaviour of the solutions of the Kassoy problem with a modified source term [Elektronische Daten] We study the asymptotic behaviour as x →∞ of the solutions of the ordinary differential equation problem This equation generalises the ordinary differential equation obtained by studying the blow-up of the similarity solutions of the semilinear parabolic partial differential equation vt=vxx = ev. We show that if λ≦1, all solutions of (*) tend to —∞ as rapidly as the function —exp (x2/4) (E- solutions). However, if λ>1, then there also exists a solution which tends to -∞, like 2λlog(x) (L-solutions). Thus, the case λ = 1, for which (*) reduces tothe Kassoy equation, is the borderline between two quite different forms of asymptotic behaviour of the function u(x). Copyright © Royal Society of Edinburgh 1989 Budd C. Oxford University, Computing Laboratory, 8-11 Keble Road, Oxford, OX1 3QD, U.K. Qi Y. Oxford University, Computing Laboratory, 8-11 Keble Road, Oxford, OX1 3QD, U.K. Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 347-356 0308-2105 113:3-4<347 1989 113 PRM https://doi.org/10.1017/S0308210500024185 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500024185 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Budd C. Oxford University, Computing Laboratory, 8-11 Keble Road, Oxford, OX1 3QD, U.K NATIONALLICENCE 700 1- Qi Y. Oxford University, Computing Laboratory, 8-11 Keble Road, Oxford, OX1 3QD, U.K NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 347-356 0308-2105 113:3-4<347 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge