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(1983)
Semigroups of linear operators and applications to partial differential equations
(2009)
RIMS Kôkyûroku Bessatsu B15
Youshan Tao, M. Winkler (2012)
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusionDiscrete and Continuous Dynamical Systems, 32
R. Schulz, P. Knabner (2017)
Derivation and analysis of an effective model for biofilm growth in evolving porous mediaMathematical Methods in the Applied Sciences, 40
(2012)
Discrete Continuous Dynam
The work is concerned with the growth of biofilms made by chemotactical bacteria within a two‐dimensional saturated porous media. The increase of a biomass on the surface of the solid matrix changes the porosity and impede the flow through the pores. By formal periodic homogenization an averaged model describing the process via Darcy's law and upscaled transport equations with effective coefficients given by the evolving microstructure at the pore‐scale was derived in [3]. Based on the assumption of uniform evolve of the underlying pore geometry and slight self‐diffusivity of the bacteria, solvability in a weak sense global in time or at least up to a possible clogging phenomenon can be shown. Furthermore, by assuming sufficient regularity on the data we prove boundedness of the solution. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Dec 1, 2017
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