Identifiability of an unknown coefficient in a nonlinear diffusion equation
Author:
M. Choulli
Journal:
Quart. Appl. Math. 47 (1989), 9-16
MSC:
Primary 35P30; Secondary 35K55
DOI:
https://doi.org/10.1090/qam/987891
MathSciNet review:
987891
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Abstract: We consider the problem of identifying an unknown coefficient in a one-dimensional diffusion equation from overspecified data measured in the interior of the domain. We obtain an identifiability result which is used to derive a uniqueness result for the inverse problem.
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J. R. Cannon and P. Duchateau, An inverse problem for a nonlinear diffusion equation, SIAM J. Appl. Math. 39, 272–289 (1980)
P. Duchateau, Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation, SIAM J. Appl. Math. 41, 310–323 (1981)
P. Duchateau, Boundary behavior and monotonicity estimates for solutions to nonlinear diffusion equations, Rocky Mountain J. Math. 15, 769–786 (1985)
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence (1968)
O. A. Ladyzhenskaya, Équations quasi-linéaires de types elliptiques et paraboliques, Colloque International ${n^ \circ }$ 117 sur les équations aux dérivées partielles, Centre National de la Recherche Scientifique, Paris, 1963
M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967
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Article copyright:
© Copyright 1989
American Mathematical Society
