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

This paper is concerned with a singular limit of the Kobayashi-Warren-Cartersystem, a phase field system modelling the evolutions of structures of grains.Under a suitable scaling, the limit system is formally derived when theinterface thickness parameter tends to zero. Different from many otherproblems, it turns out that the limit system is a system involving fractionaltime derivatives, although the original system is a simple gradient flow. Arigorous derivation is given when the problem is reduced to a gradient flow ofa single-well Modica-Mortola functional in a one-dimensional setting.

Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system