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arXiv · 2305.00525

Stability for backward problems in time for degenerate parabolic equations

Piermarco Cannarsa·Masahiro Yamamoto
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Abstract

For solution $u(x,t)$ to degenearte parabolic equations in a bounded domain $\Omega$ with homogenous boundary condition, we consider backward problems in time: determine $u(\cdot,t_0)$ in $\Omega$ by $u(\cdot,T)$, where $t$ is the time variable and $0\le t_0 < T$. Our main results are conditional stability under boundedness assumptions on $u(\cdot,0)$. The proof is based on a weighted $L^2$-estimate of $u$ whose weight depends only on $t$, which is an inequality of Carleman's type. Moreover our method is applied to semilinear degenerate parabolic equations.

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Piermarco Cannarsa, Masahiro Yamamoto. 2023-04-30. Stability for backward problems in time for degenerate parabolic equations. https://arxiv.org/abs/2305.00525

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