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Based on the perfectly matched layer (PML) technique, this paper develops a highly accurate boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media i...
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, 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...
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, (1) A multiple s...
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...
This work proposes an accurate hyper-singular boundary integral equation method for dynamic poroelastic problems with Neumann boundary condition in three dimensions and both the direct and indirect me...
This work proposes an accurate hyper-singular boundary integral equation method for dynamic poroelastic problems with Neumann boundary condition in three dimensions and both the direct and indirect me...
A temporally second-order accurate, fully discrete finite element method is proposed and analyzed for the magnetohydrodynamic (MHD) equations. A modified Crank-Nicolson method is used to discretize th...
介绍非线性科学与计算机发展关系-可积系统,探讨我们提出的可积深度学习的理论架构和发展方向。介绍我们有关可积深度学习的研究工作:基于PINN算法并对其改进,研究可积方程中的多孤子,高阶呼吸子,高阶怪波,周期背景下的高阶怪波,向量多孤子,孤子分子及其动力学行为;提出了基于守恒律的两阶段PINN算法,高维可积系统PINN算法、非局域可积系统PINN算法。
在本报告中, 我们首先介绍一个带有内部跳跃条件的二阶常微分方程特征值问题, 并将说明该特征值问题等价于一个带有 Dirac 势测度的测度微分方程特征值问题. 进而我们考虑更一般的带有 Dirac 势测度的测度微分方程特征值问题, 并且给出主特征值的存在性定理. 其次, 我们介绍带有内部跳跃条件的 logistic 扩散方程, 并且给出解的存在性定理. 此外, 我们还将讨论这些问题的生物学意义。
The Cauchy problem for the barotropic compressible Navier--Stokes equations on the whole two-dimensional space with vacuum as far field density is considered. When the shear viscosity is a positive co...
Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite–Padé approximation whose unique solution is a sequence of polynomials constructed with the help of Pfaffia...
The Cauchy problem for the barotropic compressible Navier--Stokes equations on the whole two-dimensional space with vacuum as far field density is considered. When the shear viscosity is a positive co...
In this paper, based on a domain decomposition (DD) method, we shall propose an efficient two-level preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for solving the algebraic eigenvalue problem ...

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