Convergence to self-similarity in an addition model with power-like time-depend...

• Author(s): Costa, Fernando Pestana da ; Sasportes, Rafael ; Pinto, João Teixeira
• Date: 2007
• Persistent ID: http://hdl.handle.net/10400.2/1715
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): 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
• Document Type: Part of book or chapter of book
• Language: English

Description

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.