Equations with private derivatives of the first order. Goritsky A.Yu., Chechkin G.A.

The book studies equations with private derivatives of the first order. The issues of the local existence of smooth solutions of the Koshi problem for linear, quasilineous and nonlinear equations (in particular, Eikonal equations) are considered. The theory of explosive generalized solutions for the quasilinear equation with one spatial variable is described in detail. The condition of Rankin-Gygonio was bred, the condition for the admissibility of the rupture was obtained, the concepts of entropy and energy were introduced. Particular attention is paid to the solution of the problem of Riman about the breakdown of an arbitrary rupture. The comparison of viscous (dissipating) gas and gas with dispersion is given, that is, decisions of the equations of the burghers and Corteveg - de Friza are analyzed; solitone solutions are being built. The book contains a large number of original tasks and exercises, many issues are presented on the example of their solution.

The publication is intended for students studying the course of equations with private derivatives, graduate students and teachers. It can be used as a task on this topic.