A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions
Marina Ghisi, Massimo Gobbino, Alain Haraux · DOAJ (DOAJ: Directory of Open Access Journals) · 2018
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.