An evolutionary mixed variational problem with time‐dependent Tresca friction arising from multi‐layer viscoelastic contact systems

Abstract

Based on the actual mechanical characteristics of asphalt pavement, a type of multi‐layer viscoelastic contact system (MLVECS) with time‐dependent interlayer contact conditions is proposed. Then, based on the specific problem, a class of abstract evolutionary mixed variational problems is proposed, and the existence, uniqueness, continuous dependence, and boundedness of its solutions are systematically studied. Finally, based on the theoretical research results mentioned above, the relevant properties of the solution of the mixed variation formulation corresponding to MLVECS were verified. This verification provides a solid theoretical foundation for the application of this mathematical model in pavement mechanics research.