Nondecreasing solutions to doubly nonlinear equations.
In: (INdAM Conference on Optimal Control for Evolutionary PDEs and Related Topics, 20-24 June 2016, Cortona, Italy). 2017. 31-53 (Springer INdAM Series ; 22)
Nondecreasing evolution is described via the coupling of an abstract doubly nonlinear differential inclusion and a constraint on the rate. The latter is formulated by imposing the monotonicity in time of the solution with respect to a given preorder in a Hilbert space. We discuss a solution notion for this problem and prove existence and long-time behavior.