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

In this paper we study a distributed optimal control problem for a nonlocalconvective Cahn--Hilliard equation with degenerate mobility and singularpotential in three dimensions of space. While the cost functional is ofstandard tracking type, the control problem under investigation cannot easilybe treated via standard techniques for two reasons: the state system is ahighly nonlinear system of PDEs containing singular and degenerating terms, andthe control variable, which is given by the velocity of the motion occurring inthe convective term, is nonlinearly coupled to the state variable. The latterfact makes it necessary to state rather special regularity assumptions for theadmissible controls, which, while looking a bit nonstandard, are however quitenatural in the corresponding analytical framework. In fact, they areindispensable prerequisites to guarantee the well-posedness of the associatedstate system. In this contribution, we employ recently proved existence,uniqueness and regularity results for the solution to the associated statesystem in order to establish the existence of optimal controls and appropriatefirst-order necessary optimality conditions for the optimal control problem.

Optimal distributed control of a nonlocal convective Cahn-Hilliard equation by the velocity in 3D