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Global existence and convergence to a singular steady state for a semilinear heat equation

Published online by Cambridge University Press:  14 November 2011

A.A. Lacey  and
D. Tzanetis
A.A. Lacey
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
D. Tzanetis
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
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Synopsis

With certain initial and boundary conditions the solution u* to the semilinear heat equation ∂u*/∂t = ∂u* + λ * f(u*), where f is a positive superlinear function and λ is the supremum of the open spectrum for the steady state problem Δw + λf(w) = 0, is found to exist for all time and to be unbounded. Moreover u* approaches w* a singular steady state, as / tends to infinity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 289 - 305
Copyright
Copyright © Royal Society of Edinburgh 1987

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