Property $C$ and applications to inverse problems

Details Property $C$ and applications to inverse problems Property $C$ and applications to inverse problems

2009-09-02

arxiv.org/abs/0909.0523v1

Physics

Mathematical Physics

Scientific paper

Let $\ell_j:=-\frac{d^2}{dx^2}+k^2q_j(x),$ $k=const>0, j=1,2,$ $00,$ where $p\in M$ is an arbitrary fixed function, and $u_j$ solves the problem $\ell_ju_j=0,\quad 0\leq x\leq 1,\quad u'_j(0,k)=0,\quad u_j(0,k)=1.$ If $(*)$ implies $h=0$, then the pair $\{\ell_1,\ell_2\}$ is said to have property $C$ on the set $M$. This property is proved for the pair $\{\ell_1,\ell_2\}$. Applications to some inverse problems for a heat equation are given. the set $M$. This property is proved for the pair

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