带非局部低阶项非线性抛物型方程的时间最优控制

摘要

考虑一个带非局部低阶项非线性抛物型方程的时间最优控制问题.首先利用Schauder不动点定理证明了系统的适定性,然后利用Carleman不等式和Kakutani不动点定理证明了容许控制和最优控制的存在性,并且建立了时间最优控制的最大值原理.%This article is concerned with the time optimal control of a nonlinear parabolic equation with a nonlocal lower order term. The well-posedness of the system is proved by Schauder fixed point theorem. Applying Carleman inequality and Kakutani fixed point theorem, we show the existence of admissible controls and optimal control. The maximum principle for the time optimal control problem is established.