Costa, Fernando Pestana daPinto, João TeixeiraSasportes, Rafael2018-12-212019-07-212018-12Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael - On the convergence to critical scaling profiles in submonolayer deposition models. "Kinetic and Related Models" [Em linha]. ISSN 1937-5093 (Print) 1937-5077 (Online). Vol. 11, nº 6 (2018), p. 1359–13761937-50931937-5077http://hdl.handle.net/10400.2/7805In 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.engDynamics of ODEsSubmonolayer deposition modelsAsymptotic evaluation of integralsConvergence to scaling behaviorCoagulation processesjournal article10.3934/krm.2018053