This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.

中文翻译：

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辐射传热系统的零可控性

本文研究了灰色，半透明，散射和有界区域中辐射传导对流换热系统的零可控性，其中控制作用局部地作用于子集中。Banach不动点定理证明了PDE的适定性。此外，空可控性证明基于定点参数和Carleman在存在源项的情况下进行估计，并且避免了解决线性化问题。最后，通过数值实验验证了理论结果。