Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation
An inverse problem for identifying an inclusion inside an isotropic, homogeneous heat conductive medium is considered. The shape of inclusion can change time dependently. For the one space dimensional case, we developed an analogue of the probe method known for inverse boundary value problems for elliptic equations and gave a reconstruction scheme for identifying the inclusion from the Neumann to Dirichlet map.
KeywordsWeak Solution Indicator Function Unique Solvability Boundary Measurement Reconstruction Scheme
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- 4.V. D. Kupradze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, Appl. Math. Mech. 25 (1979).Google Scholar
- 6.G. M. Lieberman, Second order parabolic differential equations, World Scientific (1996).Google Scholar
- 7.J. L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications II, Springer-Verlag (1972).Google Scholar
- 8.J. Wloka, Partial differentisl equations, Cambridge Univ. Press (1987).Google Scholar