搜索结果: 61-75 共查到“偏微分方程”相关记录1918条 . 查询时间(1.051 秒)
形状优化在计算科学与工程领域具有重要的应用，如何设计满足给定目标及物理约束的区域最优形状是一个具有百年研究历史的重要课题。形状导数是构造形状优化算法的关键所在，其不仅刻画了目标泛函关于区域的扰动变化率，还为形状梯度下降算法提供下降方向，其精度严重影响形状优化算法的收敛性。本人与合作者最近在形状优化问题的离散形状导数方面取得了重要进展。形状优化问题的形状导数具有两种表示方式，一类基于区域积分，另一类...
偏微分方程约束形状优化问题的改进的边界型离散形状梯度（龚伟）
偏微分方程 约束形状优化 边界型 离散形状梯度
2023/2/22
We propose in this paper two kinds of continuity preserving discrete shape gradients of boundary type for PDE-constrained shape optimizations. First, a modified boundary shape gradient formula for sha...
退化双曲面的应变张量及匹配性（姚鹏飞）
退化双曲面 应变张量 匹配性
2023/2/22
We prove the regularity of solutions to the strain tensor equation on degenerated hyperbolic surfaces $S$ where the Gauss curvature is zero on a part of the boundary. Furthermore, we obtain the densit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problems for stochastic wave equations
随机波动方程 反问题 随机偏微分方程
2023/4/25
Stochastic wave equations describe wave motion in random environments that is common in realistic situations. In this talk, I will present our recent studies on the inverse source and potential proble...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep learning of multi-scale PDEs based on data generated from particle methods
粒子方法 数据 多尺度 偏微分方程 深度学习
2023/4/26
Solving multi-scale PDEs is difficult in high-dimensional and/or convection-dominant cases. The interacting particle methods (IPM) are shown to outperform solving PDEs directly. Examples include compu...
T-2环面上随机不可压缩欧拉方程的一个分裂半隐欧拉方法
T-2环面 随机不可压缩 欧拉方程 分裂半隐欧拉方法
2023/1/4
The main difficulty in studying numerical method for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (J. Printems. [ESAIM Math. Model. Numer. Anal. (2001)]). Alt...
This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-d full compressible Navier--Stokes equations. It is pro...
非线性轴向运动梁的边界稳定性判据
非线性 轴向运动梁 边界稳定性 判据
2023/1/4
This paper deals with, in the framework of absolute stability, boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls. The nonlinear boundary control that...
具有完全未知的外系统的热方程的输出跟踪
完全未知 外系统 热方程 输出跟踪
2023/1/4
In this paper, we consider output regulation for a 1-d heat equation where the disturbances generated from an unknown finite-dimensional exosystem enter all possible channels. We adopt adaptive observ...
可压缩欧拉方程大初值球对称具有正远场密度整体解的存在性
可压缩 欧拉方程 大初值球对称 正远场密度整体解
2023/1/4
We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density so that...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Monge-Ampère 方程Dirichlet和边界爆破问题解的研究
Monge-Ampère方程 Dirichlet 边界爆破问题解
2023/4/26
在这个报告中，我将介绍我们近些年在Monge-Ampère 方程 Dirichlet 和边界爆破问题解的研究方面所取得的最新成果。主要包括边界爆破解的存在性、全局估计、边界估计、边界渐近行为以及径向解的存在性、多解性。这些成果主要是和华北电力大学张学梅老师合作完成。
倒向随机微分方程Sinc-θ数值格式
随机微分方程 Sinc-θ 数值格式
2023/1/5
In this paper, we propose a new family of fully discrete Sinc-$\theta$ schemes for solving backward stochastic differential equations (BSDEs). More precisely, we consider the $\theta$-schemes for the ...
具有完全未知的外系统的热方程的输出跟踪（郭宝珠）
外系统 热方程 输出跟踪 完全未知
2023/2/22
In this paper, we consider output regulation for a 1-d heat equation where the disturbances generated from an unknown finite-dimensional exosystem enter all possible channels. We adopt adaptive observ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Regularity of sub-elliptic harmonic map into non-positively curved metric space
亚椭圆谐波 非正曲线 度量空间 规律性
2023/4/28
We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with non-positive curvature, and more generally into a non-positively curved...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nontrivial solutions for a quasilinear elliptic system with weight functions
权重函数 准线性 椭圆系统 非平凡解
2023/4/28
In this talk, we consider nontrivial solutions of a quasilinear elliptic system with the weight functions h(x) and f_i (x) (i = 1, 2) by applying the Nehari manifold method along with the fibrering ma...