Fréchet differentiability for a damped sine-Gordon equation
An initial boundary value problem for the damped sine-Gordon equation with a variable diffusion coefficient is considered. The aim is to identify coefficients in equation such that the solution attains a desired behavior. This leads to an optimal control problem for which the necessary condition of optimality is written in form of a variational inequality. Much effort is done to prove the Gâteaux differentiability of the solution map and the Fréchet differentiability of the objective functional.
scientific article; zbMATH DE number 5626927