Naslov
Analysis of Multi-Species Biofilm Model

Autori
Milišić, Josipa-Pina ; Zamponi, Nicola ; Daus, Esther

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, ostalo

Skup
The 20th European Conference on Mathematics for Industry (Minisymposium Mathematics in Medicine and Life Sciences)

Mjesto i datum
Budimpešta, Mađarska, 18.06.2018. - 22.06.2018

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Podatak o recenziji nije dostupan

Ključne riječi
Biofilm model, volume-filling model, entropy method, global existence of weak solutions, long-time convergence, uniqueness of solutions

Sažetak
In this talk we present our recent result on a well-posedness of a degenerate parabolic cross-diffusion model describing multi-species biofilm community. The model is proposed by Rahman, Sudarsan and Eberl. We discuss the global-in-time existence of weak solutions in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The existence proof is based on an approximation argument, the entropy inequality and compactness lemmas. Moreover, based on the entropy inequality, the large-time asymptotics of the solution to the constant steady-state is shown. Furthermore, the uniqueness of solution is proved by combining the H^1-method and the E-monotonicity technique of Gajewski. Finaly, we present some numerical simulations obtained using DUNE Numerics, the Distributed and Unified Numerics Environment which is a modular toolbox for solving partial differential equations with grid-based methods.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA