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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/15
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boundary expansion in the Loewner-Nirenberg problem
Loewner-Nirenberg problem 边界展开 利玛窦曲率
2023/4/28
We first review some classical results of the Loewner-Nirenberg problem. Then we discuss the characteristics of boundary expansion and its applications in studying the negativity of Ricci curvatures o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Space-time finite and boundary element methods for the wave equation
波动方程 时空有限元 边界元方法
2023/4/21
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions for a free boundary problem of 3-D compressible Euler equations coupled with a nonlinear Poisson equation
三维 可压缩欧拉方程 耦合 非线性泊松方程 自由边界问题 稳定性条件
2023/4/18
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Asymptotic stability of the bipolar Navier-Stokes-Poisson system with boundary
具有边界 双极 纳维-斯托克斯-泊松系统 渐近稳定性
2023/5/6
In this talk, the combined quasi-neutral and zero-viscosity limits of the two-fluid Navier-Stokes-Poisson systems (one for ion and another for electron) with boundary are rigorously proved by investig...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Eigenvalues of boundary value problems with transmission conditions and eigenparameter-dependent boundary conditions
传输条件 本征参数 相关边界条件 边值问题 本征值
2023/5/16
In this talk, we mainly show some eigenvalue properties of second order Sturm-Liouville problems and third-order boundary value problems with both transmission conditions and eigenparameter-dependent ...
2017“自由边界问题：理论和应用”国际暑期学校（2017 ISS on “Free Boundary Problems:Theory and Applications”）
2017 自由边界问题：理论和应用 国际暑期学校
2017/1/10
Free boundary problems have vast and important applications in physics, mechanics, biology, engineering, and finance, etc. At the same time, there is a great challenge in their mathematical study whic...
2017第14届“自由边界问题：理论和应用”国际会议（14th International Conference on Free Boundary Problems:Theory and Applications ）
2017 第14届 自由边界问题：理论和应用 国际会议
2017/1/10
This conference is the 14th International Conference on Free Boundary Problems: Theory and Applications, which is in the series of conferences beginning in Montecatini (Italy, 1981) and succeeding in ...
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.
We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying metrics. The flow can be used to define a one dimensional foliation on th...
BOUNDARY BEHAVIOR OF SPECIAL COHOMOLOGY CLASSES ARISING FROM THE WEIL REPRESENTATION
BOUNDARY BEHAVIOR SPECIAL COHOMOLOGY CLASSES ARISING WEIL REPRESENTATION
2015/10/14
In our previous paper [9], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces X attached to real o...
The Embedded Boundary Integral Method (EBI) for the Incompressible Navier-Stokes equations
Embedded Boundary Integral Method (EBI) Incompressible Navier Stokes equations
2015/7/15
We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible f...
Fast Algorithms for Boundary Integral Equations
Boundary integral equations Laplace equation Helmholtz equation fast algorithms fast multipole method hierarchical matrices wavelets multiscale methods multidirectional methods
2015/7/15
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
oundary integral equations Nystrom discretization Singular integrals Nearly singular integrals Fast solvers Laplace equation Stokes equation Navier equation Fast multipole method Fast Fourier transform
2015/7/14
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...