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This paper is concerned with both observability and observers for a class of systems described by the two-dimensional hyperbolic PDEs with superlinear boundary conditions which can exhibit chaos. The ...
This paper is devoted to studying two multiobjective problems for stochastic degenerate parabolic equations. The first one is a hierarchical control problem, in which the controls are classified into ...
求解偏微分方程的预处理迭代方法是计算数学近四十年的一个热门研究方向, 这一方法得以成功的关键是有效预条件子的构造。有效预条件子的构造和分析是技巧性很强的工作, 尤其是对于具强间断系数的偏微分方程, 比如对此情形多层网格预条件子和重叠区域分解预条件子的最优收敛性在理论上一直没有彻底弄清楚。在2007年R. Hiptmair和J. Xu对麦克斯韦方程提出了“辅助空间预条件子”, 这种预条件子曾引起国际...
A locally optimal preconditioned Newton-Schur method is proposed for solving symmetric elliptic eigenvalue problems. Firstly, the Steklov-Poincaré operator is used to project the eigenvalue problem on...
We present an explicit two-parameter family of finite-band Jacobi elliptic potentials given by $q\equiv A\dn(x;m)$, where $m\in(0,1)$ and $A$ can be taken to be positive without loss of generality, fo...
M. Hairer提出的正则结构理论给出了次临界条件下带有奇异噪声随机偏微分方程的局部适定性,由此开创了研究奇异随机偏微分方程的新方向。我们得到了一类没有强耗散的奇异随机偏微分方程的全局适定性,由此给出了不用Cole-Hopf变换KPZ方程的全局适定性,改进了之前的结果。进一步,我们通过随机量子化方法,得到了O(N)量子场在二维和三维的大N极限。最后,我们通过随机量子化的方法研究了量子场的扰动理论...
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...
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...
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...
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...
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...
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...
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...
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 ...

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