Dimitrios E. Tzanetis
Abstract:
We consider a non-local initial boundary-value problem
for the equation
where
represents a temperature and
is a positive and
decreasing function. It is shown that for the radially symmetric
case, if
then there exists a critical value
such that for
there is no stationary solution and
blows up, whereas for
there exists at least one stationary solution.
Moreover, for the Dirichlet problem with
there exists a unique stationary
solution which is asymptotically stable. For the Robin problem, if
then there are at least two solutions, while if
at least one solution.
Stability and blow-up of these solutions are examined
in this article.
Submitted October 2, 2001. Published February 1, 2002.
Math Subject Classifications: 35B30, 35B40, 35K20, 35K55, 35K99.
Key Words: Nonlocal parabolic equations, blow-up, global existence,
steady states.
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Dimitrios E. Tzanetis Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80 Athens, Greece e-mail: dtzan@math.ntua.gr |
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