Existence and uniqueness of an inverse problem for a second order hyperbolic equation

Abstract

In this paper, an initial boundary value problem for a second order hyperbolic equation is considered. Giving an additional condition, a time-dependent coefficient multiplying a linear term is determined and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem numerically.

Keywords

• second order hyperbolic equation
• inverse problem
• finite difference method
• finite difference method