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arXiv · 2112.01861

Matlab program method of computing Carleman estimates and applications

Xiaoyu Fu·Yuan Gao·Qingmei Zhao
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Abstract

In this paper, we introduce a Matlab program method to compute Carleman estimate for the fourth order partial differential operator $γ\partial_t+\partial_x^4\ (γ\in\mathbb{R})$. We obtain two kinds of Carleman estimates with different weight functions, i.e. singular weight function and regular weight function, respectively. Based on Carleman estimate with singular weight function, one can obtain the known controllability and observability results for the 1-d fourth order parabolic-type equation, while based on Carleman estimate with regular weight function, one can deduce not only the known result on conditional stability in the inverse problem of half-order fractional diffusion equation, but also a new result on conditional stability in the inverse problem of half-order fractional Schrödinger equation.

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Xiaoyu Fu, Yuan Gao, Qingmei Zhao. 2021-12-11. Matlab program method of computing Carleman estimates and applications. https://arxiv.org/abs/2112.01861

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