Riv. Mat. Univ. Parma, Vol. 9, No. 1, 2018
Linda Maria De Cave^{[a]} and Marta Strani^{[b]}
Asymptotic behavior of interface solutions to semilinear parabolic equations with nonlinear forcing terms
Pages: 85131
Received: 12 March 2018
Accepted in revised form: 7 August 2018
Mathematics Subject Classification (2010): 35B25, 35B36, 35B40, 35K45.
Keywords: Metastability, slow motion, internal interfaces, asymptotic dynamics, semilinear diffusion.
Authors address:
[a]: Universität Zürich, Winterthurerstrasse 190, CH8057 Zürich, Switzerland.
[b]: Università Ca' Foscari, Dipartimento di Scienze Molecolari e Nanosistemi, Via Torino 155, 30172, Venezia Mestre, Italy.
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Abstract:
We investigate the asymptotic behavior of solutions to semilinear 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 onedimensional motion, describing the slow convergence of the interfaces
towards the equilibrium.
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