The agenda of next meetings of Krasil'shchik's seminar on geometry of
differential equations at the Independent University of Moscow.

On 7 June the seminar meets offline in room 303 of the Independent
University of Moscow, on 19:20 MSK, simultaneously, there will be
broadcast via Zoom.

Speaker: Svetlana Mukhina
Title: Contact vs symplectic geometry
Language: English
Zoom:
https://us06web.zoom.us/j/8817121842?pwd=OE5QQmNhUzNycTQvRW9ERVJ6dEliQT09
Zoom Passcode: 0706

Abstract:

The report will show how some symplectic Monge-Ampère type equations can
be solved by applying contact transformations to them.

As is known, symplectic Monge-Ampère equations with two independent
variables are locally symplectic equivalent to linear equations with
constant coefficients if and only if the corresponding Nijenhuis bracket
is zero (the Lychagin-Rubtsov theorem). Necessary and sufficient
conditions for the contact equivalence of the general (not necessarily
symplectic) Monge-Ampère linear equations were found by Kushner.

Using these results, we consider the problem of constructing exact
solutions to some equations arising in filtration theory. We will
consider a model of unsteady displacement of oil by a solution of active
reagents. This model describes the process of oil extraction from
hard-to-recover deposits. This model is described by a hyperbolic system
of partial differential equations of the first order of the Jacobi type.
Unknown functions are the water saturation and concentration of reagents
in an aqueous solution, and independent variables are time and linear
coordinate.

With the help of symplectic and contact transformations, it is possible
to reduce the model equations to a linear wave equation. The exact
solution of this system is obtained and the Cauchy problem is solved.


The seminar meets on Wednesday evenings at 19:20 MSK in room 303
and in Zoom, Meeting ID: 88 17 12 1842
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FROM 211.161.218.*