Seminars and Colloquia Schedule

Stability and bifurcation in a reaction–diffusion model with nonlocal delay effect

Series
CDSNS Colloquium
Time
Monday, August 17, 2015 - 23:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shangjiang Guo – College of Mathematics and Econometrics, Hunan University
In this talk, the existence, stability, and multiplicity of spatially nonhomogeneous steady-state solution and periodic solutions for a reaction–diffusion model with nonlocal delay effect and Dirichlet boundary condition are investigated by using Lyapunov–Schmidt reduction. Moreover, we illustrate our general results by applications to models with a single delay and one-dimensional spatial domain.

Stability of wave patterns to the bi-polar Vlasov-Poisson-Boltzmann system

Series
PDE Seminar
Time
Tuesday, August 18, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yi Wang – AMSS, Chinese Academy of Sciences
We investigate the nonlinear stability of elementary wave patterns (such as shock, rarefaction wave and contact discontinuity, etc) for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the elementary wave patterns to the system. Then, the time-asymptotic stability of the planar rarefaction wave, viscous shock waves and viscous contact wave (viscous version of contact discontinuity) are proved for the 1D bipolar Vlasov-Poisson-Boltzmann system. These results imply that these basic wave patterns are still stable in the transportation of charged particles under the binary collision, mutual interaction, and the effect of the electrostatic potential force. The talk is based on the joint works with Hailiang Li (CNU, China), Tong Yang (CityU, Hong Kong) and Mingying Zhong (GXU, China).

Time-Domain Boundary Element Methods for Acoustic Problems - Sound Radiation from Tyres

Series
School of Mathematics Colloquium
Time
Thursday, August 20, 2015 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Dr. Ernst Stephan – Leibniz University Hannover –

Special time.

We consider the time-domain boundary element method for exterior Robin type boundary value problems for the wave equation. We apply a space-time Galerkin method, present a priori and a posteriori error estimates, and derive an h-adaptive algorithm in space and time with mesh refinement driven by error indicators of residual and hierarchical type. Numerical experiments are also given which underline our theoretical results. Special emphasis is given to numerical simulations of the sound radiation of car tyres.

On typical motion of piecewise smooth systems

Series
CDSNS Colloquium
Time
Friday, August 21, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cinzia Elia – Università degli Studi di Bari
In this talk we examine the typical behavior of a trajectory of a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. It is well known that (in the class of Filippov vector fields, and under commonly occurring conditions) one may anticipate sliding motion on $\Sigma$. However, this motion itself is not in general uniquely defined, and recent contributions in the literature have been trying to resolve this ambiguity either by justifying a particular selection of a Filippov vector field or by substituting the original discontinuous problem with a regularized one. However, in this talk, our concern is different: we look at what we should expect of a typical solution of the given discontinuous system in a neighborhood of $\Sigma$. Our ultimate goal is to detect properties that are satisfied by a sufficiently wide class of discontinuous systems and that (we believe) should be preserved by any technique employed to define a sliding solution on $\Sigma$.

Towards a structure theory for immersions

Series
ACO Colloquium
Time
Friday, August 21, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Paul Wollan – University of Rome "La Sapienza"

Refreshments will be served in the atrium immediately following the talk. Please join us to welcome the new class of ACO students.

Graph immersion is an alternate model for graph containment similar to graph minors or topological minors. The presence of a large clique immersion in a graph G is closely related to the edge connectivity of G. This relationship gives rise to an easy theorem describing the structure of graphs excluding a fixed clique immersion which serves as the starting point for a broader structural theory of excluded immersions. We present the highlights of this theory with a look towards a conjecture of Nash-Williams on the well-quasi-ordering of graphs under strong immersions and a conjecture relating the chromatic number of a graph and the exclusion of a clique immersion.