Stability analysis of partial differential variational inequalities in Banach spaces

In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.