Article Dans Une Revue Advances in Nonlinear Analysis Année : 2018

A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions

Marina Ghisi
  • Fonction : Auteur
Massimo Gobbino
  • Fonction : Auteur

Résumé

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 infinity), 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, and we show that the set of initial data giving rise to fast solutions is a graph of codimension one in the phase space.

Dates et versions

hal-03904571 , version 1 (16-12-2022)

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Citer

Marina Ghisi, Massimo Gobbino, Alain Haraux. A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions. Advances in Nonlinear Analysis, 2018, 7 (3), pp.375-384. ⟨10.1515/anona-2016-0171⟩. ⟨hal-03904571⟩
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