We study gradient flows in $L^2$ of general convex and lower semicontinuous functionals with linear growth. Typical examples of such evolution equations are the time-dependent minimal surface equation and the total variation flow. Classical results concerning characterisation of solutions require a special form or differentiability of the Lagrangian; we apply a duality-based method to formulate a general definition of solutions, prove their existence and uniqueness, and reduce the regularity and structure assumptions on the Lagrangian. The talk is primarily based on a joint work with José M. Mazón.