Point island dynamics under fixed rate deposition

Allen, D. and Grinfeld, M. and Sasportes, R. (2019) Point island dynamics under fixed rate deposition. Journal of Mathematical Analysis and Applications, 472 (2). pp. 1716-1728. ISSN 0022-247X (https://doi.org/10.1016/j.jmaa.2018.12.018)

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We consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.