Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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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DOI: https://doi.org/10.1090/qam/1233531
Article copyright: © Copyright 1993 American Mathematical Society


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