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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

D. E. Tzanetis
D. E. Tzanetis
Affiliation:
Department of Mathematics National Technical University Zografou Campus 15780 Athens, Greece
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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

References

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