# 13.12 Logarithmic delays in non local Fisher KPP problems. (Emeric Bouin)

Title : Logarithmic delays in non local Fisher KPP problems.

Speaker: Emeric Bouin (Université Paris-Dauphine )

Abstract : We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front starting from a localized population. Depending on the behavior of the competition kernel at infinity, the location of the front is either as in the local case, or polynomial. This is a joint work with Christopher Henderson (U. Chicago) and Lenya Ryzhik (Stanford).

Time: 10:15-11:45, 13.12. 2018

Place: C116

# 24.10 Well/ill posedness for problems in fluid mechanics (Eduard Feireisl)

Title: Well/ill posedness for problems in fluid mechanics

Speaker: Eduard Feireisl (Institute of Mathematics AS CR )

Abstract: We discuss the state of the art of well/ill posedness of problems

arising in dynamics of compressible viscous/inviscid fluids. We propose

a solution to this problem based on stochastic approach selecting a

suitable Markovian semigroup.

Time: 11:00-12:30

Place: B 6, A 303

# 27.02 Effective equations for focusing bosonic systems (Thanh Nam Phan)

Title: Effective equations for focusing bosonic systems

Speaker: Thanh Nam Phan (LMU)

Abstract: We study the effective descriptions of many-body Schroedinger dynamics of interacting bosons. To the leading order, the system exhibits the Bose-Einstein condensation and the condensate is described by a one-body nonlinear Schroedinger equation. To the second order, the excitations around the condensate are effectively described by Bogoliubov theory. I will discuss some recent results on the rigorous derivation of the effective equations. A special attention will be paid on the focusing case, where the stability of the system is not obvious.

Time: 10:15-11:45 27.02.2018

Place: C116, A5,6

# 24.01 Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system (Johannes Lankeit)

Title: Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system

Speaker: Johannes Lankeit (Paderborn)

Abstract: We consider a parabolic-elliptic chemotaxis system generalizing

\[ \begin{cases}\begin{split}

& u_t=\nabla\cdot((u+1)^{m-1}\<wbr />nabla u)-\nabla \cdot(u(u+1)^{\sigma-1}\nabla v)\\

& 0 = \Delta v - v + u

\end{split}\end{cases} \]

in bounded smooth domains $\Omega\subset \mathbb{R}^N$, $N\ge 3$, and with homogeneous Neumann boundary conditions. We show that

*) solutions are global and bounded if ${\sigma}<m-\frac{N-2}N$

*) solutions are global if $\sigma \le 0$

*) close to given radially symmetric functions there are many initial data producing unbounded solutions if $\sigma >m-\frac{N-2}N$.

In particular, if ${\sigma}\le 0$ and $\sigma > m-\frac{N-2}N$, there are many initial data evolving into solutions that blow up after infinite time.

Time: 24.01.2018 14:00-15:30

Place: A5 6, C116

# 10.01 Global existence analysis of cross-diffusion population systems for multiple species (Esther Daus)

Title: Global existence analysis of cross-diffusion population systems for multiple species

Speaker: Esther Daus (TU Wien)

Abstract: We prove the existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction), the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

This is a joint work with X. Chen and A. Juengel.

Time: 10.01.2018 9:00-10:30

Place: A5 6 C116