Semigroups of locally Lipschitz operators associated with semilinear evolution equations
Semigroups of locally Lipschitz operators associated with semilinear evolution equations
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DOI：
10.1016/j.jmaa.2006.08.028
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发表时间：
2007-06
影响因子：
1.3
通讯作者：
Yoshikazu Kobayashi;Toshitaka Matsumoto;N. Tanaka
中科院分区：
文献类型：
--
作者：
Yoshikazu Kobayashi;Toshitaka Matsumoto;N. Tanaka
在本文中，我们引入了局部 Lipschitz 算子半群的概念，它为半线性演化方程的柯西问题提供了温和的解，并刻画了这种局部 Lipschitz 算子半群。半群的概念源自微分方程的初始边值问题的适定性概念，其解算子即使在局部意义上也不是拟收缩的，而是相对于其初始数据局部 Lipschitz 连续的。所得结果应用于复数 Ginzburg-Landau 方程的初始边值问题。
In this paper we introduce the notion of semigroups of locally Lipschitz operators which provide us with mild solutions to the Cauchy problem for semilinear evolution equations, and characterize such semigroups of locally Lipschitz operators. This notion of the semigroups is derived from the well-posedness concept of the initial-boundary value problem for differential equations whose solution operators are not quasi-contractive even in a local sense but locally Lipschitz continuous with respect to their initial data. The result obtained is applied to the initial-boundary value problem for the complex Ginzburg–Landau equation.