Dynamics of Evolutionary PDE Systems

Abstract

The article is devoted to a method for constructing exact and approximate solutions of systems of partial differential evolution equations (PDE). The basis of this method is the concept of finite-dimensional dynamics, introduced for scalar equations by B. Kruglikov, O. Lychagina and V. Lychagin. The basic idea is that a system of evolution equations generates a flow in the space of solutions of some systems of ordinary differential equations. These ordinary differential equations have symmetries whose generating functions are generated by the right-hand sides of the evolutionary system. Dynamics and exact solutions for a system of evolution equations that describes processes of deep filtration of a suspension and the telegraph equation are constructed.