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- Convergence to self-similarity in an addition model with power-like time-dependent input of monomersPublication . Costa, Fernando Pestana da; Sasportes, Rafael; Pinto, João TeixeiraIn 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.
- A nonautonomous predator-prey system arising from coagulation theoryPublication . Costa, Fernando Pestana da; Pinto, João TeixeiraA recent investigation of Budác et al. on the selfsimilar behaviour of solutions to a model of coagulation with maximum size [Oxford Center for Nonlinear PdE, Report no. OxPDE-10/01, June 2010] led us to consider a related nonautonomous Lotka-Volterra predator-prey system in which the vector field of the predator equation converges to zero as t\rightarrow +\infty. The solutions of the system show a behaviour distinct from those of either autonomous or periodic analogs. A partial numerical and analytical study of these systems is initiated. An ecological interpretation of this type of systems is proposed.