Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Stability of a system of Volterra integro-differential equations

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.     

Some noncoercive parabolic equations with lower order terms in divergence form

This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div(uE), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $.AMS Subject Classification: 35K10, 35K15, 35K65.     

Existence of solutions to an anisotropic phase‐field model

We consider an anisotropic phase‐field model for the isothermal solidification of a binary alloy due to Warren–Boettinger ( Acta. Metall. Mater. 1995; 43 (2):689). Existence of weak solutions is established under a certain convexity condition on the strongly non‐linear second‐order anisotropic operator and Lipschitz and boundedness assumptions for the non‐linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non‐linearities. The qualitative properties of the solutions are illustrated by a numerical example. Copyright © 2003 John Wiley & Sons, Ltd.     

Two Dimensional Interface Problems for Elliptic Equations

We study the structure of solutions to the interface problems for second order quasi-linear elliptic partial differential equations in two dimensional space. We prove that each weak solution can be decomposed into two parts near singular points, a finite sum of functions in the form of cr^α log^m rφ(θ) and a regular one w. The coefficients c and the C^{1,α} norm of w depend on the H¹-norm and the C^{º,α}-norm of the solution, and the equation only.     

Local convergence of quasi-Newton methods for B-differentiable equations

We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples.     

求解平片裂纹问题的有限部积分与边界元法

本文利用位移的Somigliana公式和有限部积分的概念,导出了求解三维弹性力学中的任意形状平片裂纹问题的超奇异积分方程组,进而联合使用有限部积分法与边界元法对所得方程建立了数值法.为验证本文的方法,计算了若干数值例子的裂纹面的位移间断及裂纹前沿的应力强度因子,它们与理论值相比符合很好.     

二维稳态各向异性介质渗透率的反演问题

1.引 言由多孔介质的渗流理论,二维稳态各向异性介质的渗流问题满足下列偏微分方程 -div(u(x,y)(?)u(x,y))=f(x,y),(x,y)∈Ω(?)R2, (1.1)