Messoud Efendiyev (Helmholtz Zentrum, München)

Mathematical modeling of biofilms & Verifications of mathematical models with diffusion, transport and interaction terms (Part I)

mercredi 15 juin 2011, 10h00 - 12h00

Salle de réunion, espace Turing


{ATTENTION : séminaire en salle Vieussens C, au 7ème étage}

Résumé / Abstract :

{{Mathematical modeling of biofilms}}
We deal with a new class of equations arising in the modelling of
biofilms. Based on the experimental observations we will derive these
equations.The peculiarity of these equations is that they are comprises two
kind of degeneracy: porous medium as well as fast diffusion. Long time
dynamics based on the global attractors of such equations as well as
biological interpetations is discussed.
Some open problems will be discussed.

{{Verifications of mathematical models with diffusion, transport and interaction terms (Part I)}}
We developed criteria and explicit algorithm which will help experts dealing with mathematical models: to check the assumptions under which the models developed by them are realistic or not.
This criteria is applied to verifying multi-component systems arising in the mathematical modelling of the life sciences. So far such a criteria was known in mathematics only for scalar equations which cannot be extended to systems of equations.