Well-posedness for a molecular beam epitaxy model
Emerald L. da Silva D.O. Tesfahun A.
15 December 2024Academic Press Inc.
Journal of Mathematical Analysis and Applications
2024#540Issue 2
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 [1], 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.
Molecular beam epitaxy , Stochastic MBE , Well-posedness
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Department of Mathematics, Nazarbayev University, Qabanbai Batyr Avenue 53, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics, California State University, Los Angeles, 5151 State University Drive, Los Angeles, 90032, CA, United States
Department of Mathematics
Department of Mathematics
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