Research On Well-posedness For System Of Hemivariational Inequality Problems

Hemivariational inequality is a kind of nonlinear inclusion problem, which involves Clake’s differential operators. In the frame of the theory of nonlinear analysis and nonsmooth analysis, hemivariational inequality, as a powerful model, has been widely applied in unilateral contact problem, non-convex semipermeable problem, multilayer structure of stratification problem and masonry engineering mechanics problems. Due to its rich applications in practical problems, hemivariational inequality has caught much attention of many scholars at home and abroad since early of 1990 s. A lot of papers and monograghs related to hemivariational inequality have been obtained.The concept of well-posedness plays an important role in the research on optimization problems, variational inequality problems, equilibrium problems and other relative problems. It has important influence on the solvablilty, uniqueness of solution, stability analysis and design of algorithm for the corresponding problems.System of hemivational inequalities and system of split hemivational inequalities can be regarded as two kinds of generalization of hemivariational inequality. They also have many important applications in physics, engineering and economics. In this thesis, we will extend the research of well-posedness to system of hemivariational inequalities and system of split hemivariational inequality by introducing the concept of well-posedness for the corresponding problems, establishing their characterization properties and studying some equivalence results of well-posedness. This thesis is organized as below.In chapter one, within the frame of theoy of nonlinear analysis, momotone operator theory and noncompactness theory, we first give some concepts of well-posdness for the system of hemivariational inequalities by defining its approximating sequence, and then prove some properties and their relations of two defined sets under very mild hypotheses. In chapter two, based on the two sets and their properties, we establish some characterization properties for the well-posedness of system of hemivatiational inequalities. Due to the fact that the system of hemivariational inequalities can be viewed as a class of system of nonlinear inclusion problems, we study the wellposedness of system of nonlinear inclusion problems in chapter three and show some equivalence results of well-posedness between system of hemivariational inequalities and system of inclusion problems. At last, in chapter four, we study a system of split hemivariational inequalities and introduce the research of wellposedness to the system of split hemivariational inequalities. Moreover, under different monotonicity conditions, some equivalence results between the strong/weak well-posedness of system of split hemivariational inequalities and the existence and uniqueness of its solution are obtianed.