Convergence to self-similarity in an addition model with power-like time-dependent input of monomers

• Main Author: Costa, Fernando Pestana da
• Publication Date: 2007
• Other Authors: Sasportes, Rafael, Pinto, João Teixeira
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10400.2/1715
• topic: Dinâmica de EDOs não-autónomas; Equações de coagulação; Comportamento assimptótico; Comportamento auto-semelhante; Dynamics of non-autonomous ODEs; Coagulation equations; Long-time behaviour; Self-similar behaviour

In this note we extend the results published in Ref. 1 to a coagulation system with Becker-Doring type interactions and time-dependent input of monomers $J_{1}(t)$ of power–like type: $J_{1}(t)/(\alpha t^{\omega }) \rightarrow 1$ as $t \rightarrow \infty$, with $\alpha > 0$ and $\omega > − \frac{1}{2}$. The general framework of the proof follows Ref. 1 but a different strategy is needed at a number of points.