Aclass of incrementally scattering-passive nonlinear systems

We investigate a special class of nonlinear infinite dimensional systems.

These are obtained by subtracting a nonlinear maximal monotone (possibly multi-valued) operator M from the semigroup generator of a scattering passive linear system.

While the linear system may have unbounded linear damping (for instance, boundary damping) which is only densely defined, the nonlinear damping operator M is assumed to be defined on the whole state space.

We show that this new class of nonlinear infinite dimensional systems is well-posed and incrementally scattering passive.

Our approach uses the theory of maximal monotone operators and the Crandall-Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax-Phillips type nonlinear semigroup that represents the whole system.