Asymptotic behavior of interface solutions to quasilinear parabolic equations with nonlinear forcing terms
Analysis of PDEs
2015-06-30 v1
Abstract
We investigate the asymptotic behavior of solutions for quasilinear parabolic equations in bounded intervals. In particular, we are concerned with a special class of solutions, called interface solutions, which exhibit e 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.
Keywords
Cite
@article{arxiv.1506.08456,
title = {Asymptotic behavior of interface solutions to quasilinear parabolic equations with nonlinear forcing terms},
author = {Linda De Cave and Marta Strani},
journal= {arXiv preprint arXiv:1506.08456},
year = {2015}
}
Comments
32 pages, 2 figures