System of Integral Equations for Solving an Inverse Problem for a Quasilinear Hyperbolic Equation

Abstract

For a quasilinear hyperbolic equation containing a numerical parameter, we consider the inverse problem of determining an unknown function occurring in the free term of the equation. The inverse problem is reduced to a system of integral equations for the unknown function and the solution of the hyperbolic equation. We prove the existence and uniqueness of the solution of this system and of the inverse problem. The asymptotics of the solution of the system is studied for small values of the parameter occurring in the hyperbolic equation.