On the identification of the heat conductivity distribution from partial dynamic boundary measurements

ABSTRACT

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.

Keywords:

• Heat equation
• heat conductivity
• identification
• exact boundary controllability

2010 Mathematics Subject Classifications:

• 35K05
• 35R30
• 80A23
• 35B40

Disclosure statement

No potential conflict of interest was reported by the authors.