Formation and interaction of islands

It is assumed that the surface profile for t 0 is described by the finite series 

For any surface shape (9.70), the mass flux distribution is related to shape change through local mass conservation. The surface mass conservation requirement is given in (9.8) in the absence of a deposition flux. In the present instance, the mass conservation relation is modified through the inclusion of deposition flux, and it takes the form 

The optimum choice of rates dfc is the set that renders a maximum with respect to variations in those rates, which leads to a system of nonlinear ordinary differential equations for ak t) of the form 

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