Discontinuous Models of Real World Problems

Differential equations with discontinuities , which model real world problems, start to be one of the most important and interesting subject of the modern science. Originated in mechanics, and nowadays extend to electronics, medicine, biology, finance and economics, the theory of equations with discontinuous right-hand-side, impulsive differential equations, differential equations with piecewise constant argument, hybrid systems, have won strong attention of specialists. Nevertheless, some of models with discontinuities a still simple in their parts, which produce discontinuous change of motion, despite that , for example, mechanics, gives new possibilities for modeling. Consequently, we should work not only in developing of the mathematical theory, but also consider problems of modeling.