Perturbation Method for First- and Complete Second-Order Differential Equations

We are concerned with an inverse problem for a linear evolution equation of the first order. Both hyperbolic and parabolic cases will be considered. A complete second-order evolution equation will be considered together with a related identification problem. We indicate sufficient conditions for the existence and the uniqueness of a solution to these problems. All the results apply well to inverse problems for equations from mathematical physics. Indeed, as a possible application of the abstract theorems, some examples of partial differential equations are given. © 2015, Springer Science+Business Media New York.