Boundary hemivariational inequality of parabolic type Original Research Article

In this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time-dependent pseudomonotone operator. We establish the existence of solutions for such inequality. Our proof is based on a known surjectivity result for operators of pseudomonotone type. We present an example of semipermeability heat conduction problem to which the result applies.