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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Laplacian estimates for the cscK equation
cscK方程 拉普拉斯估计 Nash-Moser迭代
2023/11/29
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Unconditional stability and error estimates of FEMs for the electro-osmotic flow in micro-channels
微通道 电渗流FEM 无条件稳定性 误差估计
2023/5/15
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some recent progress on the gradient estimates for the insulated conductivity problem
绝缘 电导率 梯度估计 椭圆偏微分方程
2023/4/17
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 ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
Steklov-eigenfunctions 尖锐 Lp 估计 节点集
2023/4/13
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Carleman estimates for some stochastic partial differential equations and applications
随机 偏微分方程 卡勒曼估计
2023/5/5
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some estimates on an exterior Steklov eigenvalue problem
外部 斯特克洛夫特征值 估计
2023/5/9
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....
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
ELLIPTIC RECONSTRUCTION AND A POSTERIORI ERROR ESTIMATES FOR PARABOLIC PROBLEMS
A posteriori error estimators fi nite elements semidiscrete parabolic problems
2015/12/11
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...
GALERKIN AND RUNGE{KUTTA METHODS: UNIFIED FORMULATION, A POSTERIORI ERROR ESTIMATES AND NODAL SUPERCONVERGENCE
Continuous discontinuous Galerkin methods
2015/12/11
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...
Optimal order a posteriori error estimates for a class of Runge{Kutta and Galerkin methods
error estimates Galerkin methods
2015/12/11
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 ...
POINTWISE A POSTERIORI ERROR ESTIMATES FOR MONOTONE SEMI-LINEAR EQUATIONS
residual maximum norm
2015/12/11
We derive upper and lower a posteriori estimates for the maximum norm error in nite element solutions of monotone semi-linear equations.
The estimates hold for Lagrange elements of any xed order, n...
A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
Dispersive estimates interaction Morawetz type (correlation) estimates many-body Hamiltonian many-body Schrodinger equation quantum hydrodynamics BBGKY hierarchy
2015/10/16
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
Lp estimates for quantities advected by a compressible flow
Lp estimates quantities advected compressible flow
2015/10/15
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration...
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
ADAPTIVE SPLINE ESTIMATES FOR NONPARAMETRIC REGRESSION MODELS
ADAPTIVE SPLINE ESTIMATES NONPARAMETRIC REGRESSION MODELS
2015/8/25
ADAPTIVE SPLINE ESTIMATES FOR NONPARAMETRIC REGRESSION MODELS.