Well-posed Property of the Inverse Problem for the Lame's Parameters λ,μ and Dissipative Factor γ

Abstract

In this paper, the inversion of coefficients Lame's parameters λ, μ and dissipative factor ϒ in one order dissipative elastic wave equation in the vector form is discussed. Under some smoothness conditions, we have proved the existence, uniqueness and extension theorems of the local solution to the inverse problem by means of an equivalent integral system. Stability, well-posed property of the solution and the property of the solution at the end point of the largest existence interval are also researched.