An Inverse Coefficient Problem for an Integro-differential Equation

In this article we consider the inverse coefficient problem of recovering the function { ( x ) system of partial differential equations that can be reduced to a second order integro-differential equation $ -u_{xx} + c(x)u_{x} + dphi (x)u-gamma dphi (x)int _{0}^{t}e^{-gamma (t-tau )}u(x,tau ), dtau = 0 $ with boundary conditions. We prove the existence and uniqueness of solutions to the inverse problem and develop a numerical algorithm for solving this problem. Computational results for some examples are presented.