On the identification of the heat conductivity distribution from partial dynamic boundary measurements. (English) Zbl 1475.35414
Summary: This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary measurements and for finite interval in time. By constructing of appropriate test functions, using a control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the diffusion coefficient as the leading order of an appropriate averaging of the partial dynamic boundary measurements.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35K05 | Heat equation |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 93B05 | Controllability |
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