广义算子半群与广义分布参数系统的适定性

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.

Generalized operator semigroup and well-posedness of singular distributed parameter systems

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.