论文标题
由乘法控制控制的半线性反应扩散方程的近似可控性
Approximate controllability of the semilinear reaction-diffusion equation governed by a multiplicative control
论文作者
论文摘要
在本文中，我们关注的是由多维半延伸方程的近似可控性，该方程受乘法控制的控制，该方程在反应项中局部分布。对于给定的初始状态，我们为理想状态提供足够的条件，以便在任意较小的时间间隔内大致达到。此外，在获得全球支持的控制的情况下，我们证明了事先给出的任何时间间隔内的近似可控性，这不取决于初始状态和目标状态。我们的方法基于线性半群理论，并基于平滑函数均匀近似的结果。
In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial state we provide sufficient conditions on the desirable state to be approximately reached within an arbitrarily small time interval. Moreover, in the case of a globally supported control, we prove the approximate controllability within any time-interval given in advance which does not depend on the initial and target states. Our approaches are based on linear semigroup theory and some results on uniform approximation with smooth functions.
