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 finite-time singularities in the linear advection-diffusion equationwith a variable speed on a semi-infinite line. The variable speed is determinedby an additional condition at the boundary, which models the dynamics of acontact line of a hydrodynamic flow at a 180 contact angle. Using apriorienergy estimates, we derive conditions on variable speed that guarantee that asufficiently smooth solution of the linear advection--diffusion equation blowsup in a finite time. Using the class of self-similar solutions to the linearadvection-diffusion equation, we find the blow-up rate of singularityformation. This blow-up rate does not agree with previous numerical simulationsof the model problem.

Finite-time singularities in the dynamical evolution of contact lines