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Existence and uniqueness for a nonlinear inverse reaction‐diffusion problem with a nonlinear source in higher dimensions
Author(s) -
Akyildiz Fahir Talay,
Tatar Salih,
Ulusoy Suleyman
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2765
Subject(s) - mathematics , inverse problem , uniqueness , inverse , nonlinear system , mathematical analysis , diffusion , transformation (genetics) , geometry , physics , biochemistry , chemistry , quantum mechanics , gene , thermodynamics
This paper analyzes the existence and the uniqueness problem for an n ‐dimensional nonlinear inverse reaction‐diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator L λ is defined to establish the relation between the solution of L λ = 0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill‐posedness of the inverse problem. Copyright © 2013 John Wiley & Sons, Ltd.