Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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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.


References [Enhancements On Off] (What's this?)

  • [1] M. Choulli, Identifiability of an unknown coefficient in a nonlinear diffusion equation, Quart. Appl. Math. 47, 9-16 (1989) MR 987891
  • [2] M. Choulli, Identifiabilité d'un paramètre dans une équation parabolique non linéaire monodimensionelle, thèse de troisième cycle, Université Paul Sabatier, Toulouse, 1985
  • [3] P. Duchateau, Boundary behavior and monotonicity estimates for solutions to nonlinear diffusion equations, Rocky Mountain J. Math. 15, 769-786 (1985) MR 816491
  • [4] 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
  • [5] M. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1967 MR 0219861

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Additional Information

DOI: https://doi.org/10.1090/qam/1012267
Article copyright: © Copyright 1989 American Mathematical Society

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