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Identifiabilité d’un coefficient variable en espace dans une équation parabolique. (Identifiability of a spatially varying coefficient in a parabolic equation). (French) Zbl 0636.35086
We discuss identifiability of the spatially varying parameter \(\alpha\) in the parabolic equation \(\partial_ 1u-\partial_ x(\alpha (x)\partial_ xu)=f\), from the knowledge of the values of the state at one point \(x_ p\in [0,1]\). The function f and the boundary data are supposed to be known. The identifiability problem is formulated as an inverse Sturm-Liouville problem.
35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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