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 present an analytical study, in the one space dimensionalcase, of the fluid dynamics system proposed in [4] to model the formation ofbiofilms. After showing the hyperbolicity of the system, we show that, in aopen neighborhood of the physical parameters, the system is totally dissipativenear its unique non vanishing equilibrium point. Using this property, we areable to prove existence and uniqueness of global smooth solutions to the Cauchyproblem on the whole line for small perturbations of this equilibrium point andthe solutions are shown to converge exponentially in time at the equilibriumstate.

Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension