So far, controlling the solutions of PDE’s on fractal sets has not been much explored. Whereas those structures bear interesting properties in terms of heat diffusion. We hereafter discuss the extension of classical results of control theory to self-similar sets, and apply them to the benchmark case of the Sierpiński Gasket. Our results show that this path will gain being developped.

中文翻译：

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分形集上热方程的最优控制

到目前为止，在分形集上控制PDE的解还没有太多探索。而这些结构在热扩散方面具有令人感兴趣的特性。下文中，我们将讨论控制理论的经典结果到自相似集的扩展，并将其应用于Sierpiński垫片的基准案例。我们的结果表明，这条道路将得到发展。