In this paper, we study the approximate controllability of a class of semilinear systems governed by coupled degenerate parabolic equations. The equations may be weakly degenerate and strongly degenerate on a portion of the lateral boundary. We prove that the control systems are approximately controllable by using the Kakutani fixed point theorem and the controls can be taken to be of quasi bang-bang form.

中文翻译：

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一类半线性退化系统的近似可控性

在本文中，我们研究了一类由耦合退化简并抛物方程控制的半线性系统的近似可控性。这些方程在侧向边界的一部分上可能是弱退化的，也可能是强烈退化的。我们证明了通过使用Kakutani不动点定理，该控制系统是近似可控的，并且该控制可被认为是准bang-bang形式。