Existence of a Solution of the Inverse Coefficient Problem for a Quasilinear Hyperbolic Equation

Abstract

A problem with data on the characteristics for a quasilinear hyperbolic equation is considered. An inverse problem consisting in determining the unknown coefficient of the equation, depending on its solution, is formulated. As additional information for the inverse problem, the values of the solution of the problem with the data on the characteristics at a fixed value of one of the independent variables are specified. The existence theorem for the inverse problem is proved. The proof is based on deriving a nonlinear operator equation for the unknown coefficient and the proof of its solvability.