On one nonlocal inverse boundary problem for the Benney – Luke equation with integral conditions

Yashar Mehraliyev, Bahar Valiyeva
2019 Journal of Physics, Conference Series  
An inverse boundary value problem for the Benney-Luke equation with periodic and integral condition is investigated. The definition of a classical solution of the problem is introduced. The goal of this paper is to determine the unknown coefficient and to solve the problem of interest. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, we perform a conversion from the original problem to some auxiliary inverse problem with trivial boundary
more » ... h trivial boundary conditions. By the contraction mapping principle we prove the existence and uniqueness of solutions of the auxiliary problem. Then we make a conversion to the stated problem again and, as a result, we obtain the solvability of the inverse problem.
doi:10.1088/1742-6596/1203/1/012100 fatcat:j33ikgivozhoffegohg3p2ep3m