Regularization for Ill-posed Cauchy problems associated with generators of analytic semigroups
Regularization for Ill-posed Cauchy problems associated with generators of analytic semigroups
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DOI：
10.1016/j.jde.2004.03.035
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发表时间：
2004-08
影响因子：
2.4
通讯作者：
Yongzhong Huang;Q. Zheng
中科院分区：
文献类型：
--
作者：
Yongzhong Huang;Q. Zheng
本文研究Banach空间中稠密线性算子A的不适定Cauchy问题。我们的主要结果是：如果−A是一个解析半群的生成元，那么对于这样一个不适定的Cauchy问题，利用拟可逆性方法、分数幂和线性算子半群，存在一族正则化算子.最后给出了它在病态偏微分方程中的应用。
This paper is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. Our main result is that if −A is the generator of an analytic semigroup, then there exists a family of regularizing operators for such an ill-posed Cauchy problem by using the quasi-reversibility method, fractional powers and semigroups of linear operators. The applications to ill-posed partial differential equations are also given.