论文标题
线性反应扩散系统的状态受限的可控性
State-constrained controllability of linear reaction-diffusion systems
论文作者
论文摘要
我们研究了线性抛物线方程组的耦合系统的可控性，对状态有非负限制。我们建立了两个在巨大时间内可控性的结果：一个用于对角扩散矩阵具有“近似”的非负约束，而另一个具有“精确”非负性约束的更强的矩阵，当所有扩散系数都是相等的，而coupling矩阵的特征值则是非确定性的，则具有不含真实的实际作用。证明基于“楼梯”方法。最后，我们表明，受国家约束的可控性允许阳性的最小时间，即使对国家的单方面限制较弱。
We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an "approximate" nonnegativity constraint, and a another stronger one, with "exact" nonnegativity constraint, when all the diffusion coefficients are equal and the eigenvalues of the coupling matrix have nonnegative real part. The proofs are based on a "staircase" method. Finally, we show that state-constrained controllability admits a positive minimal time, even with weaker unilateral constraint on the state.
