caa a22 4500 388108428 CHVBK 20180307125346.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500021375 doi S0308210500021375 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500021375 The long-time behaviour of solutions to parabolic problems on unbounded intervals: the influence of boundary conditions [Elektronische Daten] For a non-negative function ū(x), we study the long-time behaviour of solutions of the heat equation with the Dirichlet or Neumann boundary conditions at x = 0. We find a critical parameter λD > 0 such that the solution subjected to the Dirichlet boundary condition tends to a spatially localized wave travelling to infinity in the space variable. On the other hand, there exists a λN > 0 such that the corresponding solution of the Neumann problem converges to a non-trivial strictly positive stationary solution. Consequently, the dynamics is considerably influenced by the choice of boundary conditions. Copyright © Royal Society of Edinburgh 1999 Fašangová Eva Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 00 Prague, Czech Republic Feireisl Eduard Institute of Mathematics AV ČR, Žitná 25, 115 67 Prague. Czech Republic Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/2(1999), 319-329 0308-2105 129:2<319 1999 129 PRM https://doi.org/10.1017/S0308210500021375 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500021375 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fašangová Eva Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 00 Prague, Czech Republic NATIONALLICENCE 700 1- Feireisl Eduard Institute of Mathematics AV ČR, Žitná 25, 115 67 Prague. Czech Republic NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/2(1999), 319-329 0308-2105 129:2<319 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge