Hamilton-Jacobi equations with a degenerate Hamiltonian coming from multipeakon problem

Zapraszamy również drugi odczyt Tomasza Cieślaka w tym samym dniu przed południem na Wydziale Matematyki Politechniki Wrocławskiej. Szczegóły poniżej. ---- Referat pt. One-dimensional fully parabolic quasilinear system of chemotaxis with critical diffusion. Streszczenie: In my talk I will speak about the system of two one-dimensional parabolic equations of Keller-Segel type with nonlinear diffusion of cells. I will be mainly focused on critical diffusion, criticality can be viewed via scaling or (un)boundedness of a natural Liapunov functional related to the problem. I will show that unlike in higher dimensions, in the case of critical diffusion all solutions (independently on the size of initial mass) are globally-in-time defined and they stay bounded. In higher dimensions one can find such a value of mass m_* s.t. for initial mass of cells smaller than m_* bounded solutions exist, while for initial mass of cells greater than m_* solutions blowup in finite-time for sufficiently concentrated data. The talk is based on two papers (T.Cieślak, K. Fujie, Proc. AMS 2018) and (B. Bieganowski, T.Cieślak, K.Fujie, T.Senba, Math. Nachr. 2019). Spotykamy się w sali 3.11, C-11, godz. 11:15.