A Space-Dependent Source Identification Problem for Hyperbolic-Parabolic Equations

In the present paper, a space-dependent source identification problem for the hyperbolic-parabolic equation with unknown parameter p &#x0024;&#x0024; \left\{ \begin{array}{l} \displaystyle u''(t) + Au(t) = p + f(t), ~ 0<t<1, \\ \displaystyle u'(t) + Au(t) = p + g(t), ~ -1<t<0, \\ \displaystyle u(0^{+})=u(0^{-}), ~ u'(0^{+})=u'(0^{-}), \\ \displaystyle u(-1)=\varphi, ~ \int \limits _{0}^{1} u(z)dz=\psi \end{array} \right. &#x0024;&#x0024;{u′′(t)+Au(t)=p+f(t),0&lt;t&lt;1,u′(t)+Au(t)=p+g(t),-1&lt;t&lt;0,u(0+)=u(0-),u′(0+)=u′(0-),u(-1)=φ,∫01u(z)dz=ψ in a Hilbert space H with self-adjoint positive definite operator A is investigated. The stability estimates for the solution of this identification problem are established. In applications, the stability estimates for the solutions of four space-dependent source identification hyperbolic-parabolic problems are obtained. © 2021, Springer Nature Switzerland AG.