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 chemo-repulsion model with quadratic production in a boundeddomain. Firstly, we obtain global in time weak solutions, and give a regularitycriterion (which is satisfied for $1D$ and $2D$ domains) to deduce uniquenessand global regularity. After, we study two cell-conservative andunconditionally energy-stable first-order time schemes: a (nonlinear andpositive) Backward Euler scheme and a linearized coupled version, provingsolvability, convergence towards weak solutions and error estimates. Inparticular, the linear scheme does not preserve positivity and the uniquenessof the nonlinear scheme is proved assuming small time step with respect to astrong norm of the discrete solution. This hypothesis is reduced to small timestep in $nD$ domains ($n\le 2$) where global in time strong estimates areproved. Finally, we show the behavior of the schemes through some numericalsimulations.

Study of a chemo-repulsion model with quadratic production. Part I: Analysis of the continuous problem and time-discrete numerical schemes