Ομιλητής : Peter Markowich (distinguished Professor of Applied Mathematics and Computational Science, King Abdullah University of Science and Technology). https://www.kaust.edu.sa/en/study/faculty/peter-markowich 

Μέρος, ώρα : Τρίτη 14/06, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.

Τίτλος : EMERGENCE OF BIOLOGICAL TRANSPORTATION NETWORKS AS A SELF-REGULATED DIFFUSION PROCESS

Περίληψη : “We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal L2-gradient flow for the symmetric tensor valued diffusivity D of abroad class of entropy dissipations associated with a purely diffusive model. The introduction of a prescribed electric potential leads to the Fokker-Planck equation, for whose entropy dissipations we also investigate the formal L2-gradient flow. We derive an integral formula for the second variation of the dissipation functional, proving convexity (in dependence of diffusivity tensor) for  a quadratic entropy density modeling Joule heating. Finally, we couple in the Poisson equation for the electric potential obtaining the Poisson-Nernst-Planck system. The formal gradient flow  of the associated entropy loss functional is derived, giving an evolution equation for D coupled with two auxiliary elliptic PDEs.”