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Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation
Published online by Cambridge University Press: 20 January 2009
Abstract
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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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 1 , February 1996 , pp. 81 - 96
- Copyright
- Copyright © Edinburgh Mathematical Society 1996
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