半线性系统的最优化问题和弱近似解  

Optimal problem and weak approximate solution of semi-linear system

作　　者：卢殿臣[1] 汤国生[1] 田立新[1] 付莲莲[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2006年第4期375-378,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(90210004);教育部骨干教师基金资助项目(BK20022003)

摘　　要：研究在D irichlet边界条件下抛物型方程的最优化问题及其弱近似解.首先给出近似解定义,利用罚函数法和Sobolev空间、变分法、偏微分方程、泛函分析等理论得出最优正则化问题解的存在性,并且以变分不等式的形式给出最优化成立的必要条件.最后构造出一个极小化序列,证明它是一弱极小化序列.从而得到弱近似解.Under Dirichlet boundary conditions, an optimal problem and weak approximate solution for a parabolic system are mainly considered. The notion of the approximate solution is given first. By using penalty method, Sobolev space,variational approach, partial differential equations, and function analysis theory, the optimal problem and the existence of the solution of the optimal regularized problem are obtained. The necessary conditions for optimality are established in the form of variational inequalities. Finally, a minimizing sequence is constructed and proved as a weak minimizing sequence. So the weak approximate solution is derived.

关 键 词：半线性抛物方程 最优控制 罚函数法 正则化 弱近似解 

分 类 号：O193[理学—数学]