Résumé: In this work, we propose a thermally coupled multiphase model for biofilm formation on a porous solid surface. The biofilm comprises a cellular phase, an extracellular-matrix phase, and interstitial water. Kinetic rates are temperature-dependent, and osmotic influx is driven by a Flory-Huggins-type swelling pressure.

Résumé: In this work, we propose a non-linear reaction-diffusion model coupled with the heat equation, modeling the action of antibiotics as well as quorum-sensing inhibitors on the virulence of bacterial biofilms in the presence of temperature effects. We prove the well-posedness of the system using semigroup theory. Then, we approximate the system by a standard finite element scheme in space and an implicit Euler method in time. Finally, numerical simulations using MATLAB are presented to validate the obtained results.

Résumé: In this work, we give the proof of the existence and uniqueness of the solution to the weak form of a two-surfaces contact problem using fixed point approach. We begin by modeling the evolution of a two deformable surfaces contact problem with a general viscoplastic law, the contact is considered frictionless and governed by the Signorini-type condition.