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

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 Hölder continuity of the weak solution is also discussed as a byproduct.

Epitaxial growth, thin film, global existence, long-time behavior, fourth-order degenerate parabolic equation, BCF step dynamics

References in corpus (1)

• Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces

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