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

• Autorzy: A. G. Ramm
• Języki publikacji: EN

Abstrakty

EN

Let $ℓ_j:= -d²/dx² + k²q_j(x)$, k = const > 0, j = 1,2, $0 < ess inf q_j(x) ≤ ess sup q_j(x) < ∞$. Suppose that (*) $∫_{0}^{1} p(x)u₁(x,k)u₂(x,k)dx = 0$ 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 $ℓ_ju_j = 0$, 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 3
• Strony: 243-249

Daty

wydano

2009

Twórcy

autor

A. G. Ramm

• Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, U.S.A.

Identyfikatory

DOI

10.4064/ba57-3-6