Messoud Efendiyev (Helmholtz Zentrum München)

Verifications of mathematical models with diffusion, transport and interaction terms (Part II) & Finite and infinite dimensional exponential attractors for degenerate equations

jeudi 16 juin 2011, 10h00 - 12h00

Salle de réunion, espace Turing


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

Résumé / Abstract :

{{Verifications of mathematical models with diffusion, transport and interaction terms (Part II)}}
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.

{{Finite and infinite dimensional exponential attractors for degenerate equations}}
In this talk we give a detailed study of the global attractor for a quite large class of degenerate parabolic equations. Not only the existence but also the infinite dimensionality of the global atractors is obtained. The upper and lower bounds for the Kolmogorov entropy of infinite-dimensional attractors are also obtained.