An inverse problem with data on the part of the boundary
| dc.creator | Ramm, A. G. | |
| dc.date | 2006-06-07 | |
| dc.date.accessioned | 2026-07-07T07:17:03Z | |
| dc.date.available | 2026-07-07T07:17:03Z | |
| dc.description | Let $u_t=\nabla^2 u-q(x)u:=Lu$ in $D\times [0,\infty)$, where $D\subset R^3$ is a bounded domain with a smooth connected boundary $S$, and $q(x)\in L^2(S)$ is a real-valued function with compact support in $D$. Assume that $u(x,0)=0$, $u=0$ on $S_1\subset S$, $u=a(s,t)$ on $S_2=S\setminus S_1$, where $a(s,t)=0$ for $t>T$, $a(s,t)\not\equiv 0$, $a\in C([0,T];H^{3/2}(S_2))$ is arbitrary. Given the extra data $u_N|_{S_2}=b(s,t)$, for each $a\in C([0,T];H^{3/2}(S_2))$, where $N$ is the outer normal to $S$, one can find $q(x)$ uniquely. A similar result is obtained for the heat equation $u_t=\mathcal{L} u:=%\triangledown \nabla \cdot (a \nabla u)$. These results are based on new versions of Property C. | |
| dc.identifier | https://arxiv.org/abs/math/0606171 | |
| dc.identifier | http://arxiv.org/abs/math/0606171 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113803 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K20, 35R30 | |
| dc.title | An inverse problem with data on the part of the boundary | |
| dc.type | text |