A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems

In this paper, we conduct a goal-oriented a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme for a semilinear elliptic problem. The a posteriori error analysis is based on variational analysis, residual errors and the adjoint problem. To carry out the analysis, we use an equivalence between the cell-centered finite volume scheme and a mixed finite element method with special choice of quadrature.     

含有一个控制的拟线性抛物系统的能控性

该文讨论了一类拟线性抛物系统的全局零能控性和逼近能控性. 文中首先给出并证明了相应的线性系统的Carleman不等式,再由Carleman不等式去证明观测不等式, 最后利用Kakutani不动点定理证明非线性系统的全局零能控性和逼近能控性.     

关于广义Beltrami方程组

该文考虑广义Beltrami方程组D~tf(x)H(x)Df(x)=J(x,f)~(2/n)G(x).(*)利用能量和变分方法,在矩阵H(x),G(x)∈S(n)满足一致椭圆型条件下,得到了(*)式所满足的齐次散度型椭圆方程DivA(x,Df(x))=0,并得到了(*)式的分量函数的弱单调性和Caccioppoli不等式.     

带有交错扩散的Leslie-Gower型三种群系统的稳态模式

讨论了带有Neumann边界条件的一类Leslie-Gower型三种群系统,在一定的条件之下,虽然系统对应的扩散(没有交错扩散)系统的唯一正平衡解是稳定的,系统中的交错扩散可导致Turing不稳定性的产生.特别地,建立了该系统非常数共存解的存在性.结果表明,交错扩散可引起系统中出现非常数正稳态解(稳态模式).     

Subalgebras Generated by all Adjoint p－nilpotent Elements and Their Normalizers in Graded Lie Algebras of Cartan Type

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New developments in frequency domain optical tomography. Part II: Application with a L-BFGS associated to an inexact line search

Gradient-based algorithms in optical tomography have shown efficiency and robustness due to their self-regularization effect, as they track the largest errors first, which tends to stabilize the reconstruction scheme. This second part shows the application of the presented developments in the first part for the reconstruction of optical properties in complex geometry while taking into account the collimated source direction with such an algorithm. The reconstruction scheme is based on the limited memory BFGS type associated to an inexact line search in order to avoid numerous evaluations of the objective function. Normalization of the objective function with measurements and independent scaling of its gradient are used to improve the quality of the reconstruction. The results show that the algorithm is efficient compared to other solvers with a better recovering of both the absorption and scattering coefficients.     

REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

Within framwork of zero-curvature representation theory,the Lax reprsentations for x- and tn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representations of the auxiliary linear problems. This method is applied to the third order spectral problem by taking modified Boussinesq hierarchy as an illustrative example.