Seminar talk, 9 November 2022

From Geometry of Differential Equations
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Speaker: Alexei Kushner

Title: On the integration of suspension filtration equations and thrombus formation

The problem of one-dimensional filtration of a suspension in a porous medium is considered. The process is described by a hyperbolic system of two first-order differential equations. This system is reduced by a change of variables to the symplectic equation of the Monge-Ampère type. It is noteworthy that this symplectic equation cannot be reduced to a linear wave equation by a symplectic transformation (the Lychagin-Rubtsov theorem works here), but it can be done by a contact transformation. This made it possible to find its exact general solution and exact solutions of the original system. The solution of the initial-boundary value problem and the Cauchy problem are constructed.

Joint work with Svetlana Mukhina.

The talk will be in Russian.