The long-time behaviour of solutions to parabolic problems on unbounded intervals: the influence of boundary conditions
1999 ◽
Vol 129
(2)
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pp. 319-329
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Keyword(s):
For a non-negative function ū(x), we study the long-time behaviour of solutions of the heat equationwith 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.
1990 ◽
Vol 13
(3)
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pp. 189-203
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Keyword(s):
2005 ◽
Vol 28
(15)
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pp. 1867-1880
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Keyword(s):
2006 ◽
pp. 209-236
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2011 ◽
Vol 4
(2)
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pp. 273-309
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Keyword(s):
1987 ◽
Vol 105
(1)
◽
pp. 117-126
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2002 ◽
Vol 18
(3)
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pp. 579-596
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2006 ◽
Vol 18
(14)
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pp. S235-S243
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Keyword(s):
2006 ◽
Vol 15
(4)
◽
pp. 1119-1135
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2011 ◽
Vol 648
(1)
◽
pp. 132-138
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Keyword(s):