Existence and convergence analysis of second-order delay differential variational–hemivariational inequalities with memory terms

Abstract

This study conducts an investigation into a generalized second-order delay differentialvariational–hemivariational inequality (SDVHI), formulated as a coupled system comprising a variational–hemivariational inequality with memory terms and a second-order delay differential equation. Initially, we establish the well-posedness of the system, proving the existence and uniqueness of solutions. Subsequently, we analyze the convergence properties of the SDVHI solutions. The practical applicability and relevance of the theoretical insights are demonstrated through a parabolic–elliptic system with an obstacle, highlighting the study’s contributions to the field.