Year: 2023
Type: preprint
Abstract: For solution $u(x,t)$ to degenearte parabolic equations in a bounded domain $Ω$ with homogenous boundary condition, we consider backward problems in time: determine $u(\cdot,t_0)$ in $Ω$ 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.
Source: arXiv (Cornell University)
Authors: Cannarsa, Piermarco, Yamamoto, Masahiro
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367694412