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 consider a partial differential equation that arises in the coarse-graineddescription of epitaxial growth processes. This is a parabolic equation whoseevolution is governed by the competition between the determinant of the Hessianmatrix of the solution and the biharmonic operator. This model might present agradient flow structure depending on the boundary conditions. We first extendprevious results on the existence of stationary solutions to this model forDirichlet boundary conditions. For the evolution problem we prove localexistence of solutions for arbitrary data and global existence of solutions forsmall data. By exploiting the boundary conditions and the variational structureof the equation, according to the size of the data we prove finite time blow-upof the solution and/or convergence to a stationary solution for globalsolutions.

Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian