Shock waves in Euler flows of gases

Abstract: Non-stationary one-dimensional Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation. Solutions obtained are multivalued and we provide a method of finding caustics, as well as wave front displacement. The method can be applied to any model of thermodynamic state as well as to any thermodynamic process. We illustrate the method on adiabatic ideal gas flows.

Russianmathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper | slides )

Geometry of differential equations seminar