English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a continuum model for solid films that arises from the modeling ofone-dimensional step flows on a vicinal surface in theattachment-detachment-limited regime. The resulting nonlinear partialdifferential equation, $u_t = -u^2(u^3+\alpha u)_{hhhh}$, gives the evolutionfor the surface slope $u$ as a function of the local height $h$ in a monotonestep train. Subject to periodic boundary conditions and positive initialconditions, we prove the existence, uniqueness and positivity of global strongsolutions to this PDE using two Lyapunov energy functions. The long timebehavior of $u$ converging to a constant that only depends on the initial datais also investigated both analytically and numerically.

A vicinal surface model for epitaxial growth with logarithmic free energy