19.12 Stability of Compressible NavierStokes/EulerMaxwell systems (Yuehong Feng)
Title: Stability of Compressible NavierStokes/EulerMaxwell systems
Speaker: Yuehong Feng (Beijing)
Abstract: In this talk, we give the long time decay rates and stabilities of solutions for Euler/NavierStokesMaxwell systems, which are partial differential equations arising from plasmas. My talk is essentially composed of three parts dealing with Cauchy problems and periodic problems. In the first part, we study the long time decay rates of the global smooth solutions for compressible EulerMaxwell systems in non isentropic case when the equilibrium solutions are constants. In the second part, we consider the stabilities of smooth solutions near non constant equilibrium states for the compressible EulerMaxwell systems. In part three, we investigate the global existence near constant equilibrium states and the stability of smooth solutions near non constant equilibrium states for the compressible NavierStokesMaxwell systems, respectively.
Time: 19.12.2017 12:3013:30
Room: A5 C116
15/16. 12. MiniWorshop: Effective equations for many particle Coulomb system
15.12.201716.12.2017, A5 6, C012
15.12.2017 Afternoon  Speaker  Topic 
14:3015:20  Merz  On the Atomic Density on the Semiclassical Length Scale in Relativistic Quantum Mechanics 
15:2016:10  Griesemer  On the dynamics of polarons in the strongcoupling limit 
16:1016:40  Coffee break  
16:4017:30  Morozov  FourierMellin theory of the relativistic massless Coulomb operator 
 
16.12.2017 Morning 


9:009:50  König  Classification of positive solutions to a 
9:5010:40  Chen  An inequality on the inverse of x projected to the positive spetral subspace of the free Dirac operator: with applications to the ionization problem of the BrownRavenhall operator 
10:4011:10  Coffee break 

11:1012:00  Liew  HewittSavage Theorem and its application in Fermionic semiclassical measures on phase space. 
 
16.12.2017 Afternoon 


14:0014:50  Wang  Some PDEs with competition effects and functional inequalities 
14:5015:40  Cuenin  Embedded eigenvalues of generalized Schrödinger operators 
15:4016:10  Coffee break 
17.10 Understanding blood cancer dynamics  insights from mathematical modeling (Thomas Stiehl)
Title: Understanding blood cancer dynamics  insights from mathematical modeling
Speaker: Thomas Stiehl (Institute of Applied Mathematics, Heidelberg University)
Abstract: Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system. The leukemic cell bulk is derived from a small and heterogeneous population of leukemic stem cells. Upon expansion, the leukemic cells outcompete healthy blood production which results in severe clinical symptoms.
To study the interaction of leukemic and healthy cells, we propose mathematical models of hierarchical cell populations. Cell competition and selection are mediated by various biologically inspired feedback mechanisms. The models relate disease dynamics to basic cell properties, such as proliferation rate (number of cell divisions per unit of time) and selfrenewal fraction (probability that a progeny of a stem cell is again a stem cell). Depending on the posed questions, we use different mathematical approaches, including nonlinear ordinary differential equations, integrodifferential equations and stochastic simulations.
A combination of mathematical analysis, computer simulations and patient data analysis provides insights in the following questions:
(1) Which mechanisms allow leukemic cells to outcompete their benign counterparts?
(2) How do leukemic stem cell properties (proliferation rate and selfrenewal fraction) affect the clinical course and patient prognosis?
(3) What can we learn about leukemic stem cell parameters using routine clinical data?
(4) What is the impact of leukemic stem cell heterogeneity on disease dynamics? Which cell properties confer selective advantages?
(5) How do leukemic cells respond to signals from their environment? Does this affect disease dynamics?
The talk is based on joint works with Anna MarciniakCzochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital).
Time: 17.10.2017, 12:0013:30
Room: A5 C116
16.08 Nonlinear Evolutionary Systems and Green's Function (Weike Wang)
Title: Nonlinear Evolutionary Systems and Green's Function
Speaker: Weike Wang (Shanghai Jiao Tong University)
Abstract: In this talk, I will show how real analysis and Green’s function method are applied for pointwise estimates of nonlinear evolutionary systems. Especially, for compressible NavierStokes equations, the general Huygan’s principle is obtained. I will also combine the Green’s function method and energy method to solve the initialboundary value problem.
Time: 16.08.2017 14:3016:00
Room: B139, A5
19.07 Meanfield limit for the KellerSegel system and the theory of propagation of Chaos (Hui Huang)
Title：Meanfield limit for the KellerSegel system and the theory of propagation of Chaos
Speaker: Hui Huang (Tsinghua University)
Abstract：We study the propagation of chaos for the Nparticle chemotaxis system subject to the Brownian diffusion. More precisely, we present a probabilistic proof of the distance between the exact microscopic and the approximate meanfiled dynamics, which leads to a derivation of the KellerSegel equation from the microscopic Nparticle system.
Time: 17.07.2017, 14:0015:30
Room: A5 C116
17.07 Fractional Laplacian and the KellerSegel system with the nonlocal diffusion (Hui Huang)
Title: Fractional Laplacian and the KellerSegel system with the nonlocal diffusion.
Speaker: Hui Huang (Tsinghua University)
Abstract: In this talk, I will give a brief introduction of the fractional Laplacian and describe our work of the KellerSegel system subject to the Levy diffusion.
Time: 17.07.2017, 14:0015:30
Room: A5 C116
05.07 Dissipative reaction diffusion systems with quadratic growth (Takashi Suzuki)
Title: Dissipative reaction diffusion systems with quadratic growth
Speaker: Takashi Suzuki (Osaka)
Abstract: We introduce a class of reaction diffusion systems of which weak solution exists globalintime with relatively compact orbit in L1. Reaction term in this class is quasipositive, dissipative, and up to with quadratic growth rate. If the space dimension is less than or equal to two, the solution is classical and uniformly bounded. Provided with the entropy structure, on the other hand, this weak solution is asymptotically spatially homogeneous. Joint work with Michel Pierre and Yoshio Yamada.
Time: 05.07.2017, 14:0015:30
Room: A5 C116
03.05 On the regularity of the 3D NavierStokes equations (Daoyuan Fang)
Title: On the regularity of the 3D NavierStokes equations
Speaker: Daoyuan Fang (School of Mathematics Sciences, Zhejiang University)
Abstract: In this talk, I will show some recent results on the 3D NavierStokes equations, which were obtained by our group during these years.
Time: 03.05.2017, 10:3012:00
Room: A5 C116
15.03 Propagation of chaos for the VlasovPoisson system (Phillip Grass)
Title: Propagation of chaos for the VlasovPoisson system
Speaker: Phillip Grass (LMU)
Abstract: The Vlasov equation is used to describe the macroscopic time evolution of a system consisting of many particles interacting by newtonian dynamics. In case of singular interaction a rigorous proof justifying this approach can be very challenging and is still an open problem for the most interesting case which is coulomb interaction. The desired result is to show that for typical initial conditions the empirical density given by the positions of the particles in phase space converges to the solution of Vlasov equation. In this talk, I will introduce a method recently developed by Boers, Lazarovici and Pickl which allows to consider the coulomb case with some cutoff depending on the particle number $N$. Additionally, I will suggest some adaptions to this approach which can be helpful to shrink the size of the $N$dependent cutoff.
Time: 15.03.2017, 10:3011:30
Room: A5 C116
03.03 Nonlinear aggregationdiffusions in the diffusiondominated and faircompetitions regimes (Jose Carrillo)
Title: Nonlinear aggregationdiffusions in the diffusiondominated and faircompetitions regimes
Speaker: Jose Antonio Carrillo (Imperial College, London)
Abstract: We analyse under which conditions equilibration between two competing effects, repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction, occurs. I will discuss several regimes that appear in aggregation diffusion problems with homogeneous kernels. I will first concentrate in the fair competition case distinguishing among porous medium like cases and fast diffusion like ones. I will discuss the main qualitative properties in terms of stationary states and minimizers of the free energies. In particular, all the porous medium cases are critical while the fast diffusion are not. In the second part, I will discuss the diffusion dominated case in which this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrisation techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the particular case of Newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregationdiffusion equations towards this unique equilibrium profile up to translations as time tends to infinity. This talk is based on works in collaboration with S. Hittmeir, B. Volzone and Y. Yao and with V. Calvez and F. Hoffmann.
Time: 03.03.2017, 15:3016:30
Room: C116
22.02 Quantitative Isoperimetric Type Inequalities and Applications (Giovanni Pisante)
Title: Quantitative Isoperimetric Type Inequalities and Applications
Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
The simplicity in the statement of the isoperimetric inequality, together with the subtle difficulties that its rigorous proof hid, had been a source of increasing interest for mathematicians. In the past decades several quantitative versions and many related applications have been presented, often with more than one proof. Aim of the lectures is to give an introduction to the classical isoperimetric inequality and to various stability results proved in recent years for this inequality and other related geometric and analytic inequalities.
Time: 22.02.2017, 10:1511:45
Room: A5 C116
15.02 On the selection of solutions to a nonlinear pde system (Giovanni Pisante)
Title: On the selection of solutions to a nonlinear pde system
Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
In the last decades a great effort has been devoted to the study of nonlinear systems of partial differential equations of implicit type. Different and quite general methods have been developed to prove the existence of almost everywhere Lipschitz regular solutions. The usual approaches are not constructive and usually, when they can be applied, provide the existence of infinitely many solutions. Thus the question of selecting a preferred solution among them raised. In the recent literature some selection criteria have been proposed to somehow minimize the irregularities of the solutions to scalar problem.
The aim of the talk is to propose a selection criterion for a particular 2dimensional vectorial problem, hoping to shade some light on the different difficulties that one can encounter when passing from the scalar to the vectorial case. We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appro priate weighted measure of some set of singularities of the gradient. The talk is based on a recent joint work with G. Croce.
Time: 15.02.2017, 10:1511:45
Room: A5 C116
08.02 Duality approach for some variational problems involving polyconvex integrands (Giovanni Pisante)
Title: Duality approach for some variational problems involving polyconvex integrands
Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
Duality methods have beed proved to be a very useful tool in the Theory of Calculus of Variations. The theory is however fully developed only in the convex setting. Several attempts have been made to try to generalize the method to nonconvex problems. Aim of the talk is to present an approach that has been recently proposed to identify dual problems for a class of polyconvex integral functionals and to discuss how this theory can be successfully applied to recover informations on the minimizers
Time: 08.02.2017, 10:1511:45
Room: A5 C116