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We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
In this talk, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profile...
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
In the statistical study of Hamiltonian PDEs out of the equilibrium (lack of invariant measures), it is a natural question to understand the transport properties for canonical Gaussian measures. The f...
Motivated by the Wisconsin octupole experiments on anomalous diffusion of hydrogen plasma across a purely poloidal octupole magnetic field, Berryman-Holland 1980 proved the stability of separable solu...
In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief int...
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
In this talk, we consider normalized solutions of nonlinear Schrodinger equations in the plane when the nonlinearity satisfies an exponential critical growth. To study the normalized solutions by usin...
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...

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