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We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density ρe. A time-di...
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
Consider the linear wave equations with a potential outside a compact set with a non-trapping boundary condition. Assuming that the potential satisfies an appropriate decreasing condition and that zer...
The antimatter counterpart of a light atomic nucleus can travel a long distance in the Milky Way without being absorbed, shows the international ALICE collaboration in an article published today in Na...
This talk is concerned with the controllability, observability and inverse problems for two types of stochastic partial differential equations, which are degenerate/singular stochastic parabolic equat...
In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain....
Holidaymakers concerned about fresh volcanic eruptions causing flight-disrupting ash clouds might be reassured by a study setting out the first reliable estimates of their frequency.While the Universi...
Carcass and price traits of 72,969 Hanwoo cows, bulls and steers aged 16 to 80 months at slaughter collected from 2002 to 2013 at 75 beef packing plants in Korea were analyzed to determine heritabilit...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm L1(0; T;L2 (Ω)): In thi...
We unify the formulation and analysis of Galerkin and Runge{Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate sol...
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge{Kutta Collocation (RK-C) methods and the continuous ...

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