When the propagation phenomena of reaction-diffusion models is considered, we always face to two questions: Can the propagation happen in every direction? Which direction is the propagation the fastest in? In this talk, we will intr...

In this talk we consider the nonnegative bounded solutions for reaction-advection-diffusion equations of the form $u_{t}-\Delta u+\alpha(t,y)u_{x}=f(t,y,u)$ in cylinders, where $f...

We study the moduli space of pairs consisting of a smooth cubic surface and a transverse plane via a period map.

In this talk, I first will introduce the linearized Energy stable and positivity preserving numerical scheme for solving Poisson-Nernst-Planck system, then provide energy stable numerical methods for solving charge transport Electrohydrodynamic (EHD) models with both Newtonian and non-Newtonian fluids. In particular, for Poisson-Nernst-Planck system, the spatial discretization is based on the reformulation of the Nernst-Planck equation, a three-level time stepping method is used to obtain the energy stability and ion concentration positivity preserving property.

Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic systems with N-peakon have been obtained, for instance, the DP equation, the Novikov equation, the Geng-Xue equation etc. In this talk, we will introduce the basic definition and some characters of peakon. Then some newly derived integrable dynamic systems with N-peakon will be presented. Meanwhile, new developments and hot points in the associated field are discussed.

In this talk, I will introduce the main results about the bounded topology of complete manifolds with nonnegative Ricci curvature and quadratically asymptotically nonnegative curvature, which will include two parts. In the first part, I will outline the results of showing such manifolds to be of finite topological type provided with some additional conditions. In the other part, I will explain the constuction of some interesting examples with such curvature conditions and infinite topology.

Mean curvature is one of the most fundamental extrinsic curvature in the theory of submanifold. A natural question is that wether mean curvature can control the area of hypersurfaces. In this talk, we discuss the area comparison with respect to mean curvature for hypersurfaces in space forms. This is a joint work with Professor Sun Jun in Wuhan University.

In this article, we investigate the (big) Hankel operators H_f on Hardy spaces of bounded strongly pseudoconvex domains in C^n  We also give a necessary and sufficient condition for boundedness of Hankel operator H_...