  We study gradient flows of general functionals with linear growth with very
weak assumptions. Classical results concerning characterisation of solutions
require differentiability of the Lagrangian, as for the time-dependent minimal
surface equation, or a special form of the Lagrangian as in the total variation
flow. We propose to study this problem using duality techniques, give a general
definition of solutions and prove their existence and uniqueness. This approach
also allows us to reduce the regularity and structure assumptions on the
Lagrangian.
