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 analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems thatarise, for example, in the modelling of biofilm growth. One of the equations,describing the evolution of a biomass density, exhibits degenerate and singulardiffusion. The other equations are either of advection-reaction-diffusion typeor ordinary differential equations. Under very general assumptions, theexistence of weak solutions is proven by considering regularized systems,deriving uniform bounds, and using fixed point arguments. Assuming additionalstructural assumptions we also prove the uniqueness of solutions.  Global-in-time well-posedness is established for Dirichlet and mixed boundaryconditions, whereas, only local well-posedness can be shown for homogeneousNeumann boundary conditions. Using a suitable barrier function and comparisontheorems we formulate sufficient conditions for finite-time blow-up or uniformboundedness of solutions. Finally, we show that solutions of the degenerateparabolic equation inherit additional global spatial regularity if thediffusion coefficient has a power-law growth.

Well-posedness and qualitative properties of quasilinear degenerate evolution systems