一类非线性集值抛物型方程的广义单调迭代法

一类非线性集值抛物型方程的广义单调迭代法 On the General Monotone Iterative Method for a Class of Set-valued Parabolic Equations 田岩 1 2 first-author 周磊 1 2 华中科技大学图像识别与人工智能研究所 华中科技大学图像识别与人工智能研究所 华中科技大学数学系,湖北,武汉,430074 华中科技大学数学系,湖北,武汉,430074 利用lakschmikantham提出的广义单调迭代法考虑了一类非线性集值抛物型方程的数值解法,利用序理论给出其迭代格式,论证了迭代解的收敛性.在局部上半Lipschitz条件下,给出了离散解集收敛性的若干结论. This paper deals with a class of nonlinear discontinuous set-valued parabolic equations by the general monotone iterative method introduced by Lakschmikantham. We discuss the convergence of the iterative solution using ordering theory after the iterative scheme is given. Furthermore, we also get some results about the convergence of the solution set under a very general condition. 集值抛物型方程 广义单调迭代法 局部上半Lipschitz条件 set-valued parabolic equation general monotone iterative method locally upper semi-Lip-schitz condition O175.29 2002-03-01 2021-04-01 3