Coupled H-semivariational Inequality And Its Application In Contact Mechanic

As an important part of inequalities,hemivariational inequalities are widely used in modeling and qualitative analysis of contact mechanics models.Using mathematical tools such as nonlinear functional analysis,nonsmooth analysis,and convex analysis,we study the existence,uniqueness,weak compactness and convergence of the solution to coupled hemivariational inequalities.Moreover,we apply theoretical knowledge to contact mechanics.Firstly,the coupled variational-hemivariational inequalities with convection terms are studied.By using upper and lower solution method,the theory of non-smooth analysis and the surjectivity theorem of multivalued mapping,the existence and boundedness of solution for the coupled system with perturbed parameters is proved.Under appropriate conditions,we prove that the solution of the original coupled system can be approximated by the solution of the perturbed problem.Secondly,a class of coupled elliptic variational-hemivariational inequalities with history-dependent operators are studied.By employing a fixed point theorem for history dependent operators and the surjectivity theorem of multivalued mapping,we establish the existence and uniqueness of solution for the coupled system.On this basis,we prove the existence,uniqueness and boundedness of the solution to the coupled system with penalty operators,and the corresponding solution sequence converges to the original coupled system solution.In addition,the theoretical results are applied to the quasi-static contact model of two elastic bodies,and the existence of weak solution is obtained.Thirdly,the coupled double-phase system with multivalued boundary conditions and non-local terms is studied.By using non-smooth analysis theory,surjectivity theorem of multivalued mapping,minty method and Kakutani-Ky Fan fixed point theorem,we establish the nonemptiness and compactness of the solution set to coupled double-phase system.Furthermore,we prove the existence,weak compactness and boundedness of solutions for coupled systems with power penalty operators and the corresponding solution sequence converges to the solution of the original coupled system.Finally,the coupled fractional hemivariational inequalities are studied.Using nonlinear functional analysis tools,the existence and boundedness of the solution to the sequential approximation problem(Rothe problem)is proved.Under appropriate conditions,the solutions of the Rothe problem converges to the solution of the original coupled system.The theoretical result is applied to the quasi-static contact model of fractionalorder viscoelastic bodies and the existence result of the weak solution is obtained.