ABSTRACT
In this chapter, we discuss fundamental results of variational inequalities including recent work of J.L.Lions on parallel algorithms of evolution variational inequalities.
Modelling, discretization, algorithms and visualization of solutions are vital components of Industrial Mathematics. In olden days, the knowledge of calculus, matrices, and differential equations was thought to be sufficient for studying modeling of problems of physics, engineering, economics, business and trade. However, in the last couple of decades several new areas of mathematics have been developed knowledge of which has become inevitable to understand and analyze properly the problems encountered in disciplines like designing and manufacturing cars, aircraft, spacecraft, railway engines and tracks, different organs of robot for hazardous industries, dams, heavy machines, life fatigue, image processing revolutionizing, electronic and computer industries; composite materials, economic and financial systems. In fact, motivation for invention of new topics in mathematics has been provided by the problems of these and many other areas.
