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C_0半群在非线性Lipschitz扰动下的范数连续性保持 被引量：2

On Persistence of Norm Continuity of Semgroups under Lipschitz Perturbations
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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.
作者 宋学力 彭济根
机构地区 长安大学理学院 西安交通大学理学院
出处 《数学的实践与认识》 CSCD 北大核心 2009年第23期208-211,共4页 Mathematics in Practice and Theory
关键词 C0半群 非线性扰动 Lipschitz半群 范数连续性 semigroups nonlinear perturbation lipschitzian semigroups norm continuity
分类号 O152.7 [理学—基础数学]
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参考文献14

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共引文献2

同被引文献13

  • 1阿拉坦仓,黄俊杰.一类无穷维Hamilton算子的半群生成定理[J].高校应用数学学报（A辑）,2006,21(3):357-364. 被引量：9
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  • 10Nagel R, Sinestrari E. Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators[J]. Lecture Notes in Pure and Applied Mathematics. New York: Marcel Dekker. 1994. 150: 51-70.

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数学的实践与认识
2009年 第23期

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