论文标题
反应扩散方程的乘法可控性，与有限的零超平面相平行
Multiplicative controllability of the reaction-diffusion equation on a parallelepiped with finitely many zero hyperplanes
论文作者
论文摘要
我们研究了平行的$ω=（a_1，b_1）\ times \ ldots（a_n，b_n）\ subset r^n $，在平行的$ω=（a_1，b_1）\ times \ ldots（a_1，b_1）\ times \ ldots（a_1，b_1）\ times r^n $中的全局近似可控性。假定初始状态$ u_0 $仅在$ω$与有限的许多超级平面的交叉点上接收零，与$ω$的侧面平行，而$ u_0 $平行于跨越此类超平面后的标志（我们进一步将它们称为“符号变化”或“零超植物的变化”）。可以将本文视为\ cite {cankh，cankh2}中提出的工作的延续，以使用有限的许多零零的解决方案的一个维反应扩散方程的可控性。但是，\ cite {cankh，cankh2}的方法本质上是一维的，而在本文中，我们引入了一种新的方法来处理多个空间变量的情况。
We study the global approximate controllability of the reaction-diffusion equation in a parallelpiped $ Ω= (a_1,b_1 ) \times \ldots (a_n,b_n) \subset R^n $, governed by a multiplicative control in a reaction term. It is assumed that the initial state $ u_0 $ admits zeros only on the intersections of $ Ω$ with finitely many hyperplanes, parallel to the sides of $ Ω$, and that $ u_0$ changes its sign after crossing such hyperplanes (we further refer to them as the "hyperplanes of change of sign" or "zero hyperplanes"). This paper can be viewed as a continuation of work presented in \cite{CanKh, CanKh2} for the controllability of the one dimensional reaction-diffusion equation with solutions admitting finitely many zeros. However, the methods of \cite{CanKh, CanKh2} are intrinsically one dimensional, while in this paper we introduce a novel approach to deal with the case of multiple spatial variables.
