We investigate the asymptotic behavior of solutions to semi-linear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit a metastable behavior, meaning that their convergence towards the asymptotic configuration of the system is exponentially slow. The key of our analysis is a linearization around an approximation of the steady state of the problem, and the reduction of the dynamics to a one-dimensional motion, describing the slow convergence of the interfaces towards the equilibrium.

Asymptotic behavior of interface solutions to semilinear parabolic equations with nonlinear forcing terms

Strani M.
2018-01-01

Abstract

We investigate the asymptotic behavior of solutions to semi-linear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit a metastable behavior, meaning that their convergence towards the asymptotic configuration of the system is exponentially slow. The key of our analysis is a linearization around an approximation of the steady state of the problem, and the reduction of the dynamics to a one-dimensional motion, describing the slow convergence of the interfaces towards the equilibrium.
2018
9
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3716993
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