A concrete realization of the slow-fast alternative for a semi linear heat equation with homogeneous Neumann boundary conditionsReport as inadecuate




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1 dm.unipi - Dipartimento di Matematica 2 dm.unipi - Dipartimento di Matematica 3 LJLL - Laboratoire Jacques-Louis Lions

Abstract : We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions.It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 exponentially as time goes to infnity, and slow solutions decaying to 0 as negative powers of t. Here we provide a characterization of slow-fast solutions in terms of their sign, andwe show that the set of initial data giving rise to fast solutions is a graph of codimension one in the phase space.





Author: Marina Ghisi - Massimo Gobbino - Alain Haraux -

Source: https://hal.archives-ouvertes.fr/



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