Seminar talk, 18 May 2011

Speaker: Rafael Sarkisyan

Title: On non-involutive points for PDEs

Abstract:
An example of algebraic PDE system $R^{q}\in J^{q}(X,V)$ is given with a semi-algebraic set $D^{q}\in R^{q}$ (this set consists of non-involutive points) such that in $D^{q}$ there are two everywhere dense subsets $A^{q}$ and $B^{q}$ having following property. While for each point $a\in A^{q}$ it is possible to divide the set of all having total order greater than $q$ partial derivatives into parametric and main part (as is the case for each involutive point of $R^{q}$), this is not possible for no one of points of $B^{q}$. We show how to state correctly an initial value problem for any point $b\in B^{q}$. This example is related with a question of V.I.Arnold.