On source identification problem for a hyperbolic-parabolic equation

Abstract

In the present paper, the boundary value problem for the differential equation with parameter $p$% \begin{equation*} \left\{ \begin{array}{l} \frac{d^{2}u(t)}{dt^{2}}+Au(t)=g(t)+p, 0<t<1, \frac{du(t)}{dt}+Au(t)=f(t)+p, -1<t<0, u(-1)=\varphi ,\text{ }u(\lambda )=\psi ,\text{ }-1<\lambda \leq 1% \end{array}% \right. \end{equation*}% in a Hilbert space $H$ with self-adjoint positive definite operator $A$ is investigated. The well-posedness of this problem is established. The stability inequalities for the solution of three source identification problems for hyperbolic-parabolic equations are obtained.