Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface

Abstract

In this work we consider $$w_t=[(w_{hh}+c_0{)}^{-3}{]}_{hh},w(0)=w^0,$$ which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that $w_{hh}$ can appear as a positive Radon measure. We prove the existence of a global strong solution. In particular, the equation holds almost everywhere when $w_{hh}$ is replaced by its absolutely continuous part.

References in corpus (2)

• Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
• Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces

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