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arXiv · 1704.05352

Distance of attractors for thin domains

José M. Arrieta·Esperanza Santamaría
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Abstract

In this work we consider a dissipative reaction-diffusion equation in a $d$-dimensional thin domain shrinking to a one dimensional segment and obtain good rates for the convergence of the attractors. To accomplish this, we use estimates on the convergence of inertial manifolds as developed previously in \cite{Arrieta-Santamaria-C0} and Shadowing theory.

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José M. Arrieta, Esperanza Santamaría. 2017-04-18. Distance of attractors for thin domains. https://doi.org/10.1016/j.jde.2017.06.023

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