Property C for ODE and Applications to an Inverse Problem for a Heat Equation

A. G. Ramm

A. G. Ramm

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009), p. 243-249 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let $ℓ_{j} : = - d ² / d x ² + k ² q_{j} (x)$ , k = const > 0, j = 1,2, $0 < e s s i n f q_{j} (x) \leq e s s s u p q_{j} (x) < \infty$ . Suppose that (*) $\int_{0}^{1} p (x) u ₁ (x, k) u ₂ (x, k) d x = 0$ 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 $ℓ_{j} u_{j} = 0$ , 0 ≤ x ≤ 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.

Publié le : 2009-01-01

Zbl 1197.34174

EUDML-ID : urn:eudml:doc:281153

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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) pp. 243-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-6/