Electron. J. Diff. Eqns., Vol. 2002(2002), No. 11, pp. 126.
Blowup of radially symmetric solutions of a nonlocal problem
modelling Ohmic heating
Dimitrios E. Tzanetis
Abstract:
We consider a nonlocal initial boundaryvalue 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 blowup 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, blowup, 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
email: dtzan@math.ntua.gr 
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