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Some remarks on the asymptotic behaviour of the solutions of a class of parabolic problems
Author(s) -
Philippin G. A.,
Proytcheva V.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.679
Subject(s) - mathematics , class (philosophy) , parabolic partial differential equation , forcing (mathematics) , exponential growth , upper and lower bounds , mathematical analysis , partial differential equation , computer science , artificial intelligence
This paper deals with a class of semilinear parabolic problems. We establish sufficient conditions on the data forcing the solution to blow up at finite time τ and derive an upper bound for τ. Moreover, we show that if the problem is modified in some way, the solution decays exponentially in time and depends continuously on the data. Copyright © 2005 John Wiley & Sons, Ltd.