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广义算子半群与广义分布参数系统的适定性
Generalized operator semigroup and well-posedness of singular distributed parameter systems
【摘要】 首先,针对广义分布参数系统的求解问题,提出了由Hilbert空间中有界线性算子所引导的广义算子半群和广义积分半群;其次,讨论了广义预解算子的性质、广义算子半群与广义积分半群的性质;最后,研究了广义分布参数系统的适定性问题.
【Abstract】 According to the solving problem of singular distributed parameter system,first of all,the generalized operator semigroup and generalized integral semigroup induced by the bounded linear operator are introduced in Hilbert space;and then the properties of the generalized resolvent operator,generalized operator semigroup,and generalized integral semigroup are discussed;at last,the well-posedness problem of the singular distributed parameter system is discussed.
【关键词】 广义算子半群;
广义积分半群;
广义分布参数系统;
适定性;
【Key words】 generalized operator semigroup; generalized integral semigroup; singular distributed parameter system; well-posedness;
【Key words】 generalized operator semigroup; generalized integral semigroup; singular distributed parameter system; well-posedness;
【基金】 国家自然科学基金(批准号:60674018)资助项目
- 【文献出处】 中国科学:数学 ,Scientia Sinica(Mathematica) , 编辑部邮箱 ,2010年05期
- 【分类号】O152.7
- 【被引频次】33
- 【下载频次】272