Determination of the leading coefficient in the heat equation

Authors:
Bei Hu and Hong-Ming Yin

Journal:
Quart. Appl. Math. **51** (1993), 577-583

MSC:
Primary 35R30; Secondary 35K05

DOI:
https://doi.org/10.1090/qam/1233531

MathSciNet review:
MR1233531

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Abstract | References | Similar Articles | Additional Information

Abstract: This note deals with the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The existence of a solution is established by means of the Schauder fixed-point theorem.

**[1]**N. Ya. Beznoshchenko,*Sufficient conditions for the existence of solutions of the problem in the determination of coefficients of the leading derivatives of parabolic equations*, Differentsial'nye Uravneniya**19**, 1908-1915 (1983) MR**723987****[2]**J. R. Cannon and R. E. Ewing,*Determination of a source term in a linear parabolic partial differential equation*, J. Appl. Math. Phys.**27**, 275-286 (1976) MR**0410089****[3]**J. R. Cannon and H. M. Yin,*A class of nonclassical parabolic problems*, J. Differential Equations**79**, 266-288 (1989) MR**1000690****[4]**J. M. Chadam and H. M. Yin,*Determination of an unknown function in a parabolic equation with an overspecifed condition*, Math. Methods Appl. Sci.**13**, 421-430 (1990) MR**1078591****[5]**D. Colton, R. E. Ewing, and W. Rundell,*Inverse problems in partial differential equations*, SIAM Proc., Philadelphia, 1990 MR**1046425****[6]**A. Friedman,*Partial differential equations of parabolic type*, Prentice Hall, Englewood Cliffs, NJ, 1964 MR**0181836****[7]**V. Isakov,*Inverse source problems*, Math. Surveys Monographs, no. 34, Amer. Math. Soc., Providence, RI, 1990 MR**1071181****[8]**W. Rundell,*The determination of a parabolic equation from the initial and final data*, Proc. Amer. Math. Soc.**99**, 637-642 (1987) MR**877031**

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Additional Information

DOI:
https://doi.org/10.1090/qam/1233531

Article copyright:
© Copyright 1993
American Mathematical Society