A characterization of boundary conditions yielding maximal monotone operators

Abstract

We provide a characterization for maximal monotone realizations for a certain class of (nonlinear) operators in terms of their corresponding boundary data spaces. The operators under consideration naturally arise in the study of evolutionary problems in mathematical physics. We apply our abstract characterization result to Port-Hamiltonian systems and a class of frictional boundary conditions in the theory of contact problems in visco-elasticity.

The definition of boundary flows was corrected. Moreover, Lemma 5.5 and Theorem 5.6 were corrected. Remark 5.7 and a sentence in the introduction referring to this Remark were erased