Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition.  prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lor triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of $j$-clusters....
['Fernando Pestana da Costa', 'João Teixeira Pinto', 'Rafael Sasportes']
I am writing a research paper on a idea RATES OF CONVERGENCE TO SCALING PROFILES IN A SUBMONOLAYER DEPOSITION MODEL AND THE PRESERVATION OF MEMORY OF THE INITIAL CONDITION
[{"from": "human", "value": "I am writing a research paper on a idea RATES OF CONVERGENCE TO SCALING PROFILES IN A SUBMONOLAYER DEPOSITION MODEL AND THE PRESERVATION OF MEMORY OF THE INITIAL CONDITION"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modeling submonolayer deposition.  prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies on a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lor triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in [Commun. Inf. Syst., 13 (2013), pp. 183--200] using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of $j$-clusters...."}]