Abstract
We consider a coagulation equation with constant coefficients and a time dependent power law input of monomers. We discuss the asymptotic behaviour of solutions as t → ∞, and we prove solutions converge to a similarity profile along the non-characteristic direction.
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References
Ablowitz, M.J., Fokas, A.S.: Complex Variables, 2nd edn. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2003)
Bartelt, M.C., Evans, J.W.: Exact island-size distributions for submonolayer deposition: influence of correlations between island size and separation. Phys. Rev. B 54, R17359–R17362 (1996)
Brilliantov, N.V., Krapivsky, P.L.: Non-scaling and source-induced scaling behaviour in aggregation models of movable monomers and immovable clusters. J. Phys. A Math. Gen. 24, 4787–4803 (1991)
Costin, O., Grinfeld, M., O’Neill, K.P., Park, H.: Long-time behaviour of point islands under fixed rate deposition. Commun. Inf. Syst. 13, 183–200 (2013)
da Costa, F.P., Sasportes, R.: Dynamics of a non-autonomous ODE system occurring in coagulation theory. J. Dyn. Differ. Equat. 20, 55–85 (2008)
da Costa, F.P., van Roessel, H., Wattis, J.A.D.: Long-time behaviour and self-similarity in a coagulation equation with input of monomers. Markov Process. Relat. Fields 12, 367–398 (2006)
Hendriks, E.M., Ernst, M.H.: Exactly soluble addition and condensation models in coagulation kinetics. J. Colloid Interface Sci. 97, 176–194 (1984)
Sasportes, R.: Dynamical problems in coagulation equations. Ph.D. Thesis, Universidade Aberta, Lisboa (2007). http://hdl.handle.net/10400.2/1909 Accessed 13 Jun 2014
Wattis, J.A.D.: Similarity solutions of a Becker-Döring system with time-dependent monomer input. J. Phys. A Math. Gen. 37, 7823–7841 (2004)
Acknowledgements
The author thanks an anonymous referee for providing insightful comments and valuable suggestions. Discussions with F.P. da Costa and J.T. Pinto are gratefully acknowledged. This work was partially supported by FCT through CAMGSD.
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Sasportes, R. (2015). Long Time Behaviour and Self-similarity in an Addition Model with Slow Input of Monomers. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Mathematics of Energy and Climate Change. CIM Series in Mathematical Sciences, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-16121-1_17
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DOI: https://doi.org/10.1007/978-3-319-16121-1_17
Publisher Name: Springer, Cham
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