具有时间依赖的时滞半线性二阶发展方程的能控性和适定性

Controllability and well posedness for second order evolution differential equations

考虑状态依赖时滞的二阶发展微分方程的能控性和适定性.首先,利用不动点定理证明状态依赖时滞的二阶发展微分方程的可控性;其次,在适当条件下证明状态依赖时滞的二阶发展微分方程是适定的;最后,通过实例验证主要结果.

This paper considers the controllability and well posedness of second order evolution differential equations with state dependent delay.Firstly,the controllability is proved for second order evolution differential equations with state dependent delay by using the fixed point theorem;Secondly,it is proved that the developed differential equation are well posed under appropriate conditions.In the end,an example is provided to represent the theory.