Differentiability of a class of semi-linear hyperbolic systems with respect to a parameter

If a parameter is contained in a hyperbolic semi-linear equation, then the solution to the equation will depend on the parameter. It is proved by using the theory of semi-groups of bounded operators that the solution continuously depends on the parameter and is Fréchet continuously differentiable, under certain mild assumptions. © 2005 Elsevier Inc. All rights reserved.