半群和线性时滞偏微分方程

SEMIGROUPS AND LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY

证明了一类线性时滞偏微分方程的mild解与相应的抽象柯西问题的mild解一一对应,并且给出了此类线性时滞偏微分方程的mild解存在唯一的充要条件.

We prove the one-to-one correspondence between mild solutions of a linear partial differential equation with delay and mild solutions of an associated abstract Cauchy problem, and give necessary and sufficient conditions for existence and uniqueness of mild solutions of the linear partial differential equation.