Dimitrios E. Tzanetis
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
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