Global structure stability of impact-induced tensile waves in phase-transforming materials

The global structure stability of the impact-induced tensile waves mentioned by Huang （Huang, S. J. Impact-induced tensile waves in a kind of phase-transforming materials. IMA Journal of Applied Mathematics, 76, 847-858 （2011）） is considered. By introducing Riemann invariants, the governing equations of motion are reduced into a 2 ~ 2 diagonally strictly hyperbolic system. Then, with the aid of the theory on the typical free boundary problem and maximally dissipative kinetics, the global structure stability of the impact-induced tensile waves propagating in a phase-transforming material is proved.     

Solvability of 2n-order m-point boundary value problem at resonance

The existence of solutions for the 2n-order m-point boundary value problem at resonance is obtained by using the coincidence degree theory of Mawhin.We give an example to demonstrate our result.The interest is that the nonlinear term may be noncontinuous.     

Global Strong Solutions for the Viscous,Micropolar, Compressible Flow

In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed initially.     

Analysis of a Free Boundary Problem Modeling Multi- Layer Tumor Growth in Presence of Inhibitor

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little Holder spaces. Next we investigate asymptotic behavior of the solution. By making delicate analysis of spectrum of the linearization of the stationary free boundary problem and using the linearized stability theorem, we prove that if the surface tension coefficient γ is larger than γ^＊ 〉 0 the fiat stationary solution is asymptotically stable provided that the constant c representing the ratio between the nutrient diffusion time and the tumor-cell doubling time is sufficient small.     

Free Boundary Value Problems for Abstract Elliptic Equations and Applications

The free boundary value problems for elliptic differential-operator equations are studied. Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L _p -spaces are given. In application, the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.     

Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics

An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.     

电化工艺中的自由边界问题

本文考虑了二个电化工艺中的自由边界问题:电加工问题和电镀问题,简要地介绍了这二个问题的数学模型和已经取得的理论成果。     

Energy Estimate for the Type-Ⅱ Superconducting Film

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high k, placed in an applied magnetic field hex, when hex is of the order of the ＂first critical field＂, i.e. of the order of ｜lnε｜. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.     

自适应隐式有限差分方法求解美式期权定价问题

本文针对美式期权的定价问题设计了基于有限差分方法的预估-校正数值算法.该算法采用显式离散格式先对自由边界条件进行预估,再对经过变量替换后的关于期权价格的偏微分方程采用隐式格式离散,并用Fourier方法分析了此离散格式的稳定性.接下来,引入基于Richardson外推法的后验误差指示子.这个后验误差指示子能够在给定的误差阈值范围内,针对期权价格和自由边界找到合适的网格划分.最后,通过设计多组数值实验并与Fazio^[1]采用显式离散格式算得的数值结果相比较,验证了所提算法的有效性,稳定性和收敛性.     

Analysis of exercise boundary of American interest rate option

By applying the variational inequality technique, we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity, boundedness and C^∞-smoothness of the exercise boundary are proved in this paper.