  In the present work we study the optimal control of an evolution equation
with non-smooth dissipation. The solution mapping of this system is non-smooth
and hence the analysis is quite challenging. Our approach is to regularize the
dissipation via approximation by a smooth function. We derive optimality
conditions for the corresponding smooth optimal control problem. Then we drive
the regularization parameter to zero and obtain necessary optimality conditions
for the original non-smooth problem. However, in this process we lose
regularity of the adjoint variables.
