Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition containing a retarded argument

摘要

We consider an initial-boundary value problem for a quasilinear system of partial differential equations with a nonlocal boundary condition containing a retarded argument. We prove a theorem on the existence and uniqueness of a solution of that problem with the use of its reduction to a system of nonlinear integro-functional equations. We study the inverse problem of finding a solution-dependent coefficient of the system on the basis of additional information on one of the components of the system solution, which is specified at a fixed point of space and is a function of time. We prove the uniqueness of the solution of the inverse problem. The proof is based on the derivation and analysis of an integro-functional equation for the difference of two solutions of the inverse problem.