Boundedness in a Biofilm-Chemotaxis Model in Evolving Porous Media

Abstract

The article concerns with a model discribing the growth of a biofilm made by chemotactical bacteria within a saturated porous media and affects the flow through the pores. The underlying model describing this process on the macroscale is derived in [21]. Therein also solvability in a weak sense and boundedness of solutions with high regularity is investigated. This current paper verifies the existence of bounded weak solutions in case of less regularity assumptions on the data.

Keywords

• evolving porous media
• biological fluid mechanics
• chemotaxis
• boundedness
• parabolic PDE