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Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime

dc.contributor.author Gao, Y
dc.contributor.author Liu, JG
dc.contributor.author Lu, J
dc.date.accessioned 2017-04-23T15:48:34Z
dc.date.available 2017-04-23T15:48:34Z
dc.date.issued 2017-04-23
dc.identifier http://arxiv.org/abs/1609.05853v2
dc.identifier.uri https://hdl.handle.net/10161/14061
dc.description.abstract We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, $ u_t=-u^2(u^3)_{hhhh}$, where $u$, considered as a function of step height $h$, is the step slope of the surface. We formulate a notion of weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of weak solution and prove it converges to a constant solution as time goes to infinity. The space-time H\"older continuity of the weak solution is also discussed as a byproduct.
dc.publisher Society for Industrial & Applied Mathematics (SIAM)
dc.subject math.AP
dc.subject math.AP
dc.subject nlin.AO
dc.title Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
dc.type Journal article
duke.contributor.id Gao, Y|0696460
duke.contributor.id Liu, JG|0437449
duke.contributor.id Lu, J|0598771
pubs.author-url http://arxiv.org/abs/1609.05853v2
pubs.notes Epitaxial growth, thin film, global existence, long-time behavior, fourth-order degenerate parabolic equation, BCF step dynamics
pubs.organisational-group Chemistry
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Physics
pubs.organisational-group Trinity College of Arts & Sciences
duke.contributor.orcid Gao, Y|0000-0002-7231-5672
duke.contributor.orcid Lu, J|0000-0001-6255-5165


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