Special Session 50: Evolution equations and inclusions with applications to control, mathematical modeling and mechanics
Contents
We deal with an abstract first order evolution inclusion in a reflexive Banach space. The inclusion contains the sum of $L$-pseudomonotone operator and a maximal monotone operator. We provide an existence theorem which is a generalization of former results known in the literature.
Next, we apply our result to the case of nonlinear variational-hemivariational inequalities considered in the setting of an evolution triple of spaces. We specify the multivalued operators in the problem and obtain existence results for several classes of variational-hemivariational inequality problems. Finally, we illustrate our existence result and study a class of quasilinear
parabolic problems under nonmonotone and multivalued flux boundary conditions.