Monotone Additive Schwarz Algorithms for Solving Two-Side Obstacle Problems

Additive Schwarz algorithms for solving the discrete problems of twrvside obstacle problems are proposed. The monotone convergence of the algorithms is established for M-matrix and the h-independent convergence rate is proved for S-matrix. The so-called finite step convergence for coincident components is discussed for nondegenerate discreted problems.

Two-side Obstacle Problem and Its Equivalent Linear Complementarity Problem

A two-side obstacle problem in R^n is an important type of variationalinequalities, which can be generated by discrete mathematical and physical problemsor some other practical models directly. Consider a two-side obstacle problem. Let f=Ax-q, . We want to find a vector x in K such

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.

Optimal obstacle control problem

In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hǒlder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1<p<2

Regularity of solutions of obstacle problems

In this paper,we improved the regularity results of obstacle problems,in which the smooth conditions of the coefficients aij(x) are released from C1() to L∞(Ω).

Optimal investment with transaction costs based on exponential utility function:a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.

Regularity of obstacle optimal control problem

In this paper, by investigating an optimal control problem which is equivalent to original problem, the regularity of an obstacle optimal control problem was treated. Furthermore, based on some properties of operator T for the variational inequality problem, the existence and uniqueness of the original problem were proved.

Residual-type a posteriori error estimate for parabolic obstacle problems

In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.

OBSTACLE PROBLEMS ON RCD(K,N)METRIC MEASURE SPACES

In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.

Numerical Solution of Obstacle Problems by B-Spline Functions

In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.

A Cubic Spline Method for Solving a Unilateral Obstacle Problem

This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically if a relation-ship between the penalty parameter and the discretization parameter h is satisfied. An error estimate between the penalty solution and the discret penalty solution is provided. To validate the theoretical results, some numerical tests on one dimensional obstacle problem are presented.

DIRICHLET PROBLEM FOR THE IMPLICIT OBSTACLE PROBLEMS

Abstract In this paper the implicit obstacle problem of fully nonlinear second order elliptic equations associated with impulsive control problem are investigated.The comparion principle for viscosity solutions is proved,the existence and uniqueness results are disscussed.

Hessian算子的Obstacle问题

本文证明了有Obstacle的Hessian方程的Dirichlet问题之W^(2,∞)解的存在性。

Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems Via a Sequence of Penalized Equations

We give an existence result of the obstacle parabolic equations3b（x,u） div（a（x,t,u, Vu））＋div（（x,t,u））=f in QT, 3twhere b（x,u） is bounded function ot u, the term atva,x,r,u, v u）） is a Letay type operator and the function is a nonlinear lower order and satisfy only the growth condition. The second term belongs to L1 （QT）. The proof of an existence solution is based on the penalization methods.

管工交叉专业改革——基于三链融合的理论视角

在智慧经济与产业创新引领下,在新文科建设的推动下,高校迫切需要对管工交叉型专业进行创新改革。文章结合天津市高校物流专业调研数据,从“历史链—组织链—目标链”三链融合理论出发,利用问卷调查进行了三链融合数据的皮尔逊相关分析,提出了管工交叉型专业改革的内在逻辑、障碍总结与路径设计。研究结果表明:以三链为基础,当前高校专业改革面临的主要障碍包括师资历史积淀少、产学研合作制度不完善、监督制度不健全、反馈制度效率低、就业升学目标不清晰以及资源组织目标不清晰等方面。因此,天津市高校应依托于教学改革、科研育人、社会服务三个模块实现数字化、智慧化、整合性人才培养目标的专业创新改革。文章结合天津大学物流工程专业改革案例,为高校管工交叉专业转型提供思路与参考。

声波移动障碍反散射问题研究

研究一种具有Dirichlet边界条件的时域声波移动障碍反散射问题。首先对时域波动方程进行求解,在有限观测时间内对移动障碍物采集动态声波近场数据;其次建立一个时域声波移动障碍反散射问题的神经网络模型,该模型将时域近场数据作为输入序列,已知形状的移动障碍物位置参数作为输出序列,求解该反散射问题;最后对于不同移动速度的情况,有效地反演出移动障碍物的位置和轨迹。数值实验表明了该方法的有效性。

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].

Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.