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

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.

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.