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A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions by Marina Ghisi; Massimo Gobbino; Alain Haraux is a Mathematics article available to read on EtoBox.

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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.

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Author

Marina Ghisi; Massimo Gobbino; Alain Haraux

Publisher

Walter de Gruyter GmbH

Published

2018

Language

EN

Field

Mathematics (Physical Sciences)