摘要
研究了基于终点观测值来反演非线性-积分抛物型方程零阶项的问题.与通常的抛物型方程系数反演问题不同,因为有非线性函数项和积分型源项的存在,使得对问题的理论研究带来一些本质性的困难.利用最优控制方法来反演该问题,首先证明控制泛函极小元的存在性,然后利用能量估计和Gronwall不等式得到极小元的必要条件,最后,由于最优控制问题的解是非凸的,故不存在全局唯一解,但通过极小元满足的必要条件及一些正问题解的先验估计,证明了极小元具有局部唯一性和稳定性.
This paper mainly studies the problem of inverting the zero-order term of nonlinear-integral parabolic equations based on terminal observations.Different from the ordinary coefficient inversion problems of parabolic equations,nonlinear function terms and integral terms had lead to some essential difficulties in the theoretical study.Therefore,the optimal control method is often adopted to invert this problem.First,the existence of the governing functional minimum element is proved,then the necessary conditions of the minimum element are obtained by using energy estimation and Gronwall’s inequality.Finally,since the solution for the optimal control problem is nonconvex,there is no unique global solution.However,it is proved that the minimum element has local uniqueness and stability through the necessary conditions satisfied by the minimal element and the prior estimates of some positive problems.
作者
许瑶瑶
杨柳
XU Yao-yao;YANG Liu(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou730070,China)
出处
《兰州交通大学学报》
CAS
2022年第6期121-126,共6页
Journal of Lanzhou Jiaotong University
基金
国家自然基金(11461039,61663018,11961042)
兰州交通大学“百名青年优秀人才培养计划”
甘肃省自然科学基金(18JR3RA122)。
关键词
非线性
最优控制
零阶项
反问题
nonlinear
optimum control
zero-order term
inverse problem
