Analyticity and observability for fractional order parabolic equations in the whole space
Analyticity and observability for fractional order parabolic equations in the whole space
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DOI：
10.1051/cocv/2023053
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Ming Wang;Can Zhang
中科院分区：
文献类型：
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作者：
Ming Wang;Can Zhang
本文研究了R^n中具有时空相依位势的分数阶抛物型方程解的定量解析性和能观性不等式。我们首先得到了上述解的空间变量关于时间变量的解析性半径的一致下界。其次，我们证明了厚集上的一个全局H“older型插值不等式，它是基于解析函数的小性传播估计。最后，我们利用伸缩级数方法从厚集上建立了一个能观性不等式。
In this paper, we study the quantitative analyticity and observability inequality for solutions of fractional order parabolic equations with space-time dependent potentials in R^n. We first obtain a uniformly lower bound of analyticity radius of the spatial variable for the above solutions with respect to the time variable. Next, we prove a globally H\''older-type interpolation inequality on a thick set, which is based on a propagation estimate of smallness for analytic functions. Finally, we establish an observability inequality from a thick set by utilizing a telescoping series method.