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Zbl 0987.35164
Ramm, A.G.
An inverse problem for the heat equation. (English)
[J] J. Math. Anal. Appl. 264, No.2, 691-697 (2001). ISSN 0022-247X

Summary: Let $u_t=u_{xx}- q(x)u$, $0\le x\le 1$, $t>0$, $u(0,t) =0$, $u(1,t)= a(t)$, $u(x,0)=0$, where $a(t)$ is a given function vanishing for $t>T$, $a(t)\not\equiv 0$, $\int^T_0a(t)dt <\infty$. Suppose one measures the flux $u_x(0,t):=b_0(t)$ for all $t>0$. Does this information determine $q(x)$ uniquely? Do the measurements of the flux $u_x(1,t): =b(t)$ give more information about $q(x)$ than $b_0(t)$ does? These questions are answered in this note.

MSC 2000:: *35R30 Inverse problems for PDE
35K05 Heat equation

Keywords: coefficient reconstruction; uniqueness; heat transfer

Cited in: Zbl 1183.35272

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