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Existence and uniqueness of an inverse problem for nonlinear Klein‐Gordon equation
Author(s) -
Tekin Ibrahim,
Mehraliyev Yashar T.,
Ismailov Mansur I.
Publication year - 2019
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.5609
Subject(s) - mathematics , uniqueness , nonlinear system , boundary value problem , mathematical analysis , klein–gordon equation , inverse problem , uniqueness theorem for poisson's equation , inverse , term (time) , geometry , physics , quantum mechanics
In this paper, an initial boundary value problem for nonlinear Klein‐Gordon equation is considered. Giving an additional condition, a time‐dependent coefficient multiplying nonlinear term is determined, and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem.