We study the kinetic roughening described by a linear diffusion equation on an initially rough substrate. We show analytically that it is not possible to write a general scaling relation valid for rough substrates. However, for a particular substrate generated by the same linear growth process, we can write a scaling relation similar to the relation valid for flat substrates, with the same growth and roughness exponents. Numerical simulations in a solid-on-solid model with surface relaxation, for $d=1,$ supports the scaling relation and the exponents.

• Received 14 May 1997

DOI:https://doi.org/10.1103/PhysRevE.56.4880