偏微分变分不等式及其应用

This project establishes the fundamental theory of partial differential (hemivariational) variational inequalities. We study the existence, uniqueness (or multiplicity) of solutions and well-posedness of partial differential (hemivariational) variational inequalities, which involve initial value, periodic, anti-periodic,nonlocal and nonlinear boundary value conditions. Furthermore, we consider the global structures and properties (such as convexity,compactness,connectedness,convergence) and dynamics properties of solutions. Develop some practical iterative algorithms for solving the partial differential (hemivariational) variational inequalities , Verify the feasibility and validity of the algorithms and new computational methods by the numerical experiments. The theoretical results obtained will be applied to the models of economics and mechanics, which can be used to provide technical support and theoretical basis for solving related practical problems.

本项目建立偏微分（H-半）变分不等式的基本理论。研究偏微分（H-半）变分不等式的初值问题、周期问题、反周期问题、非局部问题和非线性边值问题解的存在性、唯一（或多解）性以及适定性；研究解集的结构与性质（如：凸性、紧性、连通性、收敛性等）以及解的动力学行为。寻求解决这些问题的新计算方法，构造解的逼近程式，给出求数值解的迭代算法，通过数值试验证明算法的有效性。将我们获得的理论成果应用于经济学和力学模型，为解决相关实际问题提供技术支持和理论依据。

本项目建立偏微分（H-半）变分不等式的基本理论。研究偏微分（H-半）变分不等式的初值问题、周期问题、反周期问题、非局部问题和非线性边值问题解的存在性、唯一（或多解）性以及适定性；研究解集的结构与性质（如：凸性、紧性、连通性、收敛性等）以及解的动力学行为。寻求解决这些问题的新计算方法，构造解的逼近程式，给出求数值解的迭代算法，通过数值试验证明算法的有效性。将我们获得的理论成果应用于经济学和力学模型，为解决相关实际问题提供技术支持和理论依据。