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

The global existence of bounded weak solutions to a diffusion system modelingbiofilm growth is proven. The equations consist of a reaction-diffusionequation for the substrate concentration and a fourth-order Cahn-Hilliard-typeequation for the volume fraction of the biomass, considered in a bounded domainwith no-flux boundary conditions. The main difficulties are coming from thedegenerate diffusivity and mobility, the singular potential arising from alogarithmic free energy, and the nonlinear reaction rates. These issues areovercome by a truncation technique and a Browder-Minty trick to identify theweak limits of the reaction terms. The qualitative behavior of the solutions isillustrated by numerical experiments in one space dimension, using a BDF2(second-order backward Differentiation Formula) finite-volume scheme.

Existence analysis for a reaction-diffusion Cahn-Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth