一类微分算子生成的半群与发展方程初值问题的解

A Class of Semi-groups and the Solutions of Evolution Equations

本文首先给出并讨论了一类广义微分算子A_(2k)=(-1)^(k-1)D^(2k);(A_(2k-1)=(-1)^(k-1)D^(2k-1))在定义域H^(2k)(H^(2k+1)))上生成的强连续半群.讨论了算子及其生成半群的自伴性,谱性,并将其应用于发展方程Cauchy问题,给出了一类线性偏微分方程的解.

We discuss a class of strongly continuous semigroups and their infinitesimal generators-a class of sclfadjoint negative definite generalized differential operators.Applying the relation between the semi-groups and their generators to the theory of evolution equation,we obtain the solutions for a class of Cauchy problems of partial differential equations.