Determination of the leading coefficient $a(x)$ in the heat equation $u_t=a(x)\Delta u$
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: 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.
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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)
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)
J. R. Cannon and H. M. Yin, A class of nonclassical parabolic problems, J. Differential Equations 79, 266–288 (1989)
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)
D. Colton, R. E. Ewing, and W. Rundell, Inverse problems in partial differential equations, SIAM Proc., Philadelphia, 1990
A. Friedman, Partial differential equations of parabolic type, Prentice Hall, Englewood Cliffs, NJ, 1964
V. Isakov, Inverse source problems, Math. Surveys Monographs, no. 34, Amer. Math. Soc., Providence, RI, 1990
W. Rundell, The determination of a parabolic equation from the initial and final data, Proc. Amer. Math. Soc. 99, 637–642 (1987)
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Article copyright:
© Copyright 1993
American Mathematical Society
