Uniqueness result for an unknown coefficient in a nonlinear diffusion problem
Author:
M. Choulli
Journal:
Quart. Appl. Math. 47 (1989), 429-433
MSC:
Primary 35R30; Secondary 35K55
DOI:
https://doi.org/10.1090/qam/1012267
MathSciNet review:
MR1012267
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this article we develop a number of monotonicity estimates of the solution to certain nonlinear diffusion equations. These estimates are then applied to prove a uniqueness result for an unknown diffusion coefficient from overspecified data measured on the boundary. Techniques presented here are based on arguments using the maximum principle.
- M. Choulli, Identifiability of an unknown coefficient in a nonlinear diffusion equation, Quart. Appl. Math. 47 (1989), no. 1, 9–16. MR 987891, DOI https://doi.org/10.1090/S0033-569X-1989-0987891-6
M. Choulli, Identifiabilité d’un paramètre dans une équation parabolique non linéaire monodimensionelle, thèse de troisième cycle, Université Paul Sabatier, Toulouse, 1985
- Paul DuChateau, Boundary behavior and monotonicity estimates for solutions to nonlinear diffusion equations, Rocky Mountain J. Math. 15 (1985), no. 4, 769–786. MR 816491, DOI https://doi.org/10.1216/RMJ-1985-15-4-769
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Translations of Mathematical Monographs, vol. 23, Amer. Math. Soc., Providence, 1968
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
M. Choulli, Identifiability of an unknown coefficient in a nonlinear diffusion equation, Quart. Appl. Math. 47, 9–16 (1989)
M. Choulli, Identifiabilité d’un paramètre dans une équation parabolique non linéaire monodimensionelle, thèse de troisième cycle, Université Paul Sabatier, Toulouse, 1985
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 Quasi-linear Equations of Parabolic Type, Translations of Mathematical Monographs, vol. 23, Amer. Math. Soc., Providence, 1968
M. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1967
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35R30,
35K55
Retrieve articles in all journals
with MSC:
35R30,
35K55
Additional Information
Article copyright:
© Copyright 1989
American Mathematical Society
