Applic. Analysis, 81, N4, (2002), 929-937

Details Applic. Analysis, 81, N4, (2002), 929-937 Applic. Analysis, 81, N4, (2002), 929-937

2003-01-31

arxiv.org/abs/math-ph/0301045v1

Applic. Analysis, 81, N4, (2002), 929-937

Physics

Mathematical Physics

9pp

Scientific paper

Completeness of the set of products of the derivatives of the solutions to the equation $(av')'-{\l}v=0, v(0,\l)=0$ is proved. This property is used to prove the uniqueness of the solution to an inverse problem of finding conductivity in the heat equation $\dot{u}=(a(x)u')', u(x,0)=0, u(0,t)=0,\ u(1,t)=f(t)$ known for all $t>0$, from the heat flux $a(1)u'(1,t)=g(t)$. Uniqueness of the solution to this problem is proved. The proof is based on Property C. It is proved the inverse that the inverse problem with the extra data (the flux) measured at the point, where the temperature is kept at zero, (point $x=0$ in our case) does not have a unique solution, in general.

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