Geodesic
Property C for ODE and Applications to an Inverse Problem for a Heat Equation
A. G. Ramm1
1 Department of Mathematics Kansas State University Manhattan, KS 66506-2602, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 3, pp. 243-249

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\ell_j:=-{d^2}/{dx^2}+k^2q_j(x),$ $k={\rm const}>0$, $j=1,2,$ $0 \mathop{\rm ess\,inf} q_j(x)\leq \mathop{\rm ess\,sup} q_j(x)\infty.$ Suppose that $(*)\kern.5em \int_0^1p(x)u_1(x,k)u_2(x,k)\,dx=0$ for all $k>0,$ where $p$ is an arbitrary fixed bounded piecewise-analytic function on $[0,1]$, which changes sign finitely many times, and $u_j$ solves the problem $\ell_ju_j=0,\ 0\leq x\leq 1,\ u'_j(0,k)=0,\ u_j(0,k)=1.$ It is proved that $(*)$ implies $p=0$. This result is applied to an inverse problem for a heat equation.
DOI : 10.4064/ba57-3-6
Keywords: ell const mathop ess inf leq mathop ess sup infty suppose * kern int where arbitrary fixed bounded piecewise analytic function which changes sign finitely many times solves problem ell leq leq proved * implies result applied inverse problem heat equation

A. G. Ramm 1

1 Department of Mathematics Kansas State University Manhattan, KS 66506-2602, U.S.A. 
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A. G. Ramm. Property C for ODE and Applications to an Inverse 
Problem for a Heat Equation. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 3, pp. 243-249. doi: 10.4064/ba57-3-6

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