Well-posedness for a molecular beam epitaxy model

Louis Emerald, Daniel Oliveira da Silva, Achenef Tesfahun

2024

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DOI 10.1016/j.jmaa.2024.128617

Data confidence 70 medium

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Abstract

We study a general molecular beam epitaxy (MBE) equation modeling the epitaxial growth of thin films. We show that, in the deterministic case, the associated Cauchy problem admits a unique smooth solution for all time, given initial data in the space X0=L2(Rd)∩W˙1,4(Rd) with d=1,2. This improves a recent result by Agélas [3], who established global existence in H3(Rd). Moreover, we investigate the local existence and uniqueness of solutions in the space X0 for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable.