19.12 Stability of Compressible Navier-Stokes/Euler-Maxwell systems (Yuehong Feng)

Title: Stability of Compressible Navier-Stokes/Euler-Maxwell systems

Speaker: Yuehong Feng (Beijing)

Abstract: In this talk, we give the long time decay rates and stabilities of solutions for Euler/Navier-Stokes-Maxwell 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 Euler-Maxwell 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 Euler-Maxwell 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 Navier-Stokes-Maxwell systems, respectively.

Time: 19.12.2017 12:30-13:30

Room: A5 C116

15/16. 12. Mini-Worshop: Effective equations for many particle Coulomb system

15.12.2017-16.12.2017,    A5 6, C012

 

15.12.2017 Afternoon

Speaker

Topic

14:30-15:20

Merz

On the Atomic Density on the Semiclassical Length Scale in

Relativistic Quantum Mechanics

15:20-16:10

Griesemer

On the dynamics of polarons in the strong-coupling limit

16:10-16:40

Coffee break

16:40-17:30

Morozov

Fourier-Mellin theory of the relativistic massless Coulomb operator

 

16.12.2017 Morning

 

 

9:00-9:50

König

Classification of positive solutions to a
nonlinear biharmonic equation with critical exponent

9:50-10:40

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 Brown-Ravenhall operator

10:40-11:10

Coffee break

 

11:10-12:00

Liew

Hewitt-Savage Theorem and its application in Fermionic semi-classical measures on phase space.

 

16.12.2017 Afternoon

 

 

14:00-14:50

Wang

Some PDEs with competition effects and functional inequalities

14:50-15:40

Cuenin

Embedded eigenvalues of generalized Schrödinger operators

15:40-16:10

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 out-compete 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 self-renewal 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, integro-differential 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 out-compete their benign counterparts?
(2) How do leukemic stem cell properties (proliferation rate and self-renewal 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 Marciniak-Czochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital).

Time: 17.10.2017,  12:00-13:30

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 Navier-Stokes equations, the general Huygan’s principle is obtained. I will also combine the Green’s function method and energy method to solve the initial-boundary value problem.

Time: 16.08.2017 14:30-16:00

Room: B139, A5

19.07 Mean-field limit for the Keller-Segel system and the theory of propagation of Chaos (Hui Huang)

Title:Mean-field limit for the Keller-Segel system and the theory of propagation of Chaos

Speaker: Hui Huang (Tsinghua University)

Abstract:We study the propagation of chaos for the N-particle chemotaxis system subject to the Brownian diffusion. More precisely, we present a probabilistic proof of the distance between the exact microscopic and the approximate mean-filed dynamics, which leads to a derivation of the Keller-Segel equation from the microscopic N-particle system.

Time: 17.07.2017, 14:00-15:30

Room: A5 C116

17.07 Fractional Laplacian and the Keller-Segel system with the nonlocal diffusion (Hui Huang)

Title:  Fractional Laplacian and the Keller-Segel 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 Keller-Segel system subject to the Levy diffusion.

Time: 17.07.2017, 14:00-15:30

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 global-in-time with relatively compact orbit in L1. Reaction term in this class is quasi-positive, 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, 14:00-15:30

Room: A5 C116

03.05 On the regularity of the 3D Navier-Stokes equations (Daoyuan Fang)

Title:  On the regularity of the 3D Navier-Stokes equations

Speaker: Daoyuan Fang (School of Mathematics Sciences, Zhejiang University)

Abstract: In this talk, I will show some recent results on the 3D Navier-Stokes equations, which were obtained by our group during these years.

Time: 03.05.2017, 10:30-12:00

Room: A5 C116

15.03 Propagation of chaos for the Vlasov-Poisson system (Phillip Grass)

Title:  Propagation of chaos for the Vlasov-Poisson 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 cut-off 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 cut-off.

Time: 15.03.2017, 10:30-11:30

Room: A5 C116

03.03 Nonlinear aggregation-diffusions in the diffusion-dominated and fair-competitions regimes (Jose Carrillo)

Title: Nonlinear aggregation-diffusions in the diffusion-dominated and fair-competitions 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 aggregation-diffusion 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, 15:30-16:30

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, 10:15-11:45

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 2-dimensional 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, 10:15-11:45

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 non-convex 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, 10:15-11:45

Room: A5 C116

Research activities

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