Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bellout, Stability result for the inverse transmissivity problem, J. Math. Anal. Appli. No.168 13–27 (1992).
A. Elayyan and V. Isakov, On uniqueness of recovery of the discontinuous conductivity coefficient of a parabolic equation, SIAM. J. Math. Anal. 28 No.1 49–59 (1997).
M. Ikehata, Reconstruction of inclusion from boundary measurements, J.Inverse and Ill-Posed Problems, 10 (2002) 37–65.
V. D. Kupradze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, Appl. Math. Mech. 25 (1979).
P. D. Lax, A stability theorem for solutions of abstract differetial equations, and its application to the study of the local behavior of solutions of elliptic equations, Comm. Pure and Appl. Math. Vol. IX 747–766 (1956).
G. M. Lieberman, Second order parabolic differential equations, World Scientific (1996).
J. L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications II, Springer-Verlag (1972).
J. Wloka, Partial differentisl equations, Cambridge Univ. Press (1987).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer
About this chapter
Cite this chapter
Daido, Y., Kang, H., Nakamura, G. (2008). Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation. In: Aoki, T., Majima, H., Takei, Y., Tose, N. (eds) Algebraic Analysis of Differential Equations. Springer, Tokyo. https://doi.org/10.1007/978-4-431-73240-2_10
Download citation
DOI: https://doi.org/10.1007/978-4-431-73240-2_10
Received:
Revised:
Accepted:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-73239-6
Online ISBN: 978-4-431-73240-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)