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Tytuł:
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Global, Unbounded Solutions to a Parabolic Equation
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Autorzy:
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Lacey, A.A.
Tzanetis, D.E.
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Źródło:
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Journal of Differential Equations; January 1993, Vol. 101 Issue: 1 p80-102, 23p
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Nonlinear parabolic equations of the form ut = Δu + ƒ(u) and which are capable of exhibiting blow-up are considered. We find that if there is a unique steady state then it is possible to choose initial conditions so that the solution is unbouded but exists, at least in a weak sense, for all time. For more restricted problems, e.g., ƒ(u) = eu in three dimensions, we find some particular solutions to the equation which blow up at a finite time but continue to exist afterwards.Copyright 1993, 1999 Academic Press