Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation
1996 ◽
Vol 39
(1)
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pp. 81-96
Keyword(s):
Blow Up
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The initial-boundary value problem for the nonlinear heat equation u1 = Δu + λf(u) might possibly have global classical unbounded solutions, for some “critical” initial data . The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x;λ) for some values of λ We find, for radial symmetric solutions, that u*(r, t)→w(r) for any 0<r≤l but supu*(·, t) = u*(0, t)→∞, as t→∞. Furthermore, if , where is some such critical initial data, then û = u(x, t; û0) blows up in finite time provided that f grows sufficiently fast.
2005 ◽
Vol 2005
(2)
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pp. 87-94
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1972 ◽
Vol 26
(2)
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pp. 219-239
2002 ◽
Vol 13
(3)
◽
pp. 321-335
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2003 ◽
Vol 3
(1)
◽
pp. 45-58
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2002 ◽
Vol 13
(3)
◽
pp. 337-351
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2010 ◽
Vol 07
(02)
◽
pp. 297-316
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2016 ◽
Vol 103
(1)
◽
pp. 23-37
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