Author(s): Costa, Fernando Pestana da ; Pinto, João Teixeira ; Sasportes, Rafael
Date: 2018
Persistent ID: http://hdl.handle.net/10400.2/7805
Origin: Repositório Aberto da Universidade Aberta
Subject(s): Dynamics of ODEs; Submonolayer deposition models; Asymptotic evaluation of integrals; Convergence to scaling behavior; Coagulation processes
In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size $n\geq 2$ for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was studied outside of a critical direction $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi:= (x − \tau )/ \tau$ , corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau \to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.
