On the existence of solutions for amorphous molecular beam epitaxy
type: Item
instance of: scholarly article
title: On the existence of solutions for amorphous molecular beam epitaxy
zbMATH Open document ID: 1027.60063
DOI: 10.1016/S1468-1218(01)00013-X
author: D. Blömker
author: Christoph Gugg
published in: Nonlinear Analysis. Real World Applications
publication date: 2003-05-25T00:00:00Z
review text: This article deals with the following surface growth equation arising in molecular beam epitaxy \[ \partial_{t}h(t,x)=-\Delta^2h(t,x)-\mu\Delta h(t,x)-\Delta|\nabla h(t,x)|^2+\xi(t,x), \] where \(h:[0,T]\times[0,L]^{d}\rightarrow R\), \(d=1,2\), is subject to periodic boundary conditions and the initial condition \(h(0,\cdot)=h_0(\cdot)\). The stochastic term \(\xi\) is a Gaussian space-time white noise. In the case \(d=1\) the global existence of a martingale solution to the considered problem is proved. First, an approximating sequence of stochastic ordinary differential equations is solved and its boundedness in certain norms is shown. The results of Prokhorov and Skorokhod enable the authors to pass to a converging subsequence and the limit turns out to be a martingale solution of the considered problem.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1915789
zbMATH Keywords: molecular beam epitaxy
zbMATH Keywords: space-time white noise
zbMATH Keywords: martingale solution
zbMATH Keywords: Galerkin approximation
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915789