C_0半群在非线性Lipschitz扰动下的范数连续性保持  

On Persistence of Norm Continuity of Semgroups under Lipschitz Perturbations

作　　者：宋学力[1,2] 彭济根[2] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]西安交通大学理学院,陕西西安710049

出　　处：《数学的实践与认识》2009年第23期208-211,共4页Mathematics in Practice and Theory

摘　　要：研究有界线性算子强连续半群在非线性Lipschitz扰动下的正则性质保持问题.具体地,我们证明:如果强连续半群是直接范数连续的,则非线性扰动半群是直接Lipschitz范数连续的.结论推广了线性算子半群的范数连续性质保持,丰富和完善了非线性算子半群的理论.The paper is devoted to property persistence of strongly continuous semigroups of linear bounded operators under Lipschitz perturbations.Particularly,we prove that the nonlinearly perturbed semigroup is immediately Lipschitz norm continuous if the linear strongly continuous semigroup is immediately norm continuous.The result derived extends persistence of norm continuity of linear strongly continuous semigroups and enriches theory of semigroups of nonlinear operators.

关 键 词：C0半群 非线性扰动 Lipschitz半群 范数连续性 

分 类 号：O152.7[理学—数学]