Gaelle Pincet Mailly, Jean-Francois Rault
Abstract:
We study the blow-up phenomena for positive solutions of nonlinear
reaction-diffusion equations including a nonlinear convection term
in a bounded
domain of
under the dissipative dynamical boundary
conditions
.
Some conditions on g and f are discussed to state if the positive
solutions blow up in finite time or not. Moreover, for certain
classes of nonlinearities, an upper-bound for the blow-up time
can be derived and the blow-up rate can be determined.
Submitted July 10, 2012. Published January 9, 2013.
Math Subject Classifications: 35K55, 35B44.
Key Words: Nonlinear parabolic problem; dynamical boundary conditions;
lower and upper-solution; blow-up; global solution.
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Gaëlle Pincet Mailly LMPA Joseph Liouville FR 2956 CNRS Université Lille Nord de France 50 rue F. Buisson, B. P. 699, F-62228 Calais Cedex, France email: mailly@lmpa.univ-littoral.fr | |
Jean-Fran&ccdil;ois Rault LMPA Joseph Liouville FR 2956 CNRS Université Lille Nord de France 50 rue F. Buisson, B. P. 699, F-62228 Calais Cedex, France email: jfrault@lmpa.univ-littoral.fr |
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