Seminar talk, 18 May 2011: Difference between revisions

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{{Talk
{{Talk
| speaker = Rafael Sarkisyan
| speaker = Rafael Sarkisyan
| title = On non-involutive points for PDEs
| title = A remark on the Cartan-Kahler theorem
| abstract = The talk will discuss an example of algebraic PDE system <math>R^q \in J^{q}(X,V)</math> endowed with a semi-algebraic set <math>D^q \in R^q</math> (this set consists of non-involutive points) such that in <math>D^q</math> there are two everywhere dense subsets <math>A^q</math> and <math>B^q</math> having the following property.  While for each point <math>a \in A^q</math> it is possible to divide the set of partial derivatives of total order greater than <math>q</math> into parametric and main part (as is the case for each involutive point of <math>R^q</math>), this is not possible for points of <math>B^q</math>.  We show how to state correctly  an initial value problem for any point <math>b \in B^q</math>.  This example is related with a question of V.I.Arnold.
| abstract = The talk will discuss an example of algebraic PDE system <math>R^q \subset J^{q}(X,V)</math> and a semi-algebraic set <math>D^q \subset R^q</math> (this set consists of non-involutive points) such that in <math>D^q</math> there are two everywhere dense subsets <math>A^q</math> and <math>B^q</math> having the following property.  While for each point <math>a \in A^q</math> it is possible to divide the set of partial derivatives of total order greater than <math>q</math> into parametric and main part (as in the case of involutive points of <math>R^q</math>), this is not possible for points of <math>B^q</math>.  We show how to state correctly  an initial value problem for any point <math>b \in B^q</math>.  This example is related to a question of V.I.Arnold.
| slides =  
| slides =  
| references =  
| references =  
| 79YY-MM-DD = 7988-94-81
| 79YY-MM-DD = 7988-94-81
}}
}}

Latest revision as of 14:12, 12 May 2011

Speaker: Rafael Sarkisyan

Title: A remark on the Cartan-Kahler theorem

Abstract:
The talk will discuss an example of algebraic PDE system and a semi-algebraic set (this set consists of non-involutive points) such that in there are two everywhere dense subsets and having the following property. While for each point it is possible to divide the set of partial derivatives of total order greater than into parametric and main part (as in the case of involutive points of ), this is not possible for points of . We show how to state correctly an initial value problem for any point . This example is related to a question of V.I.Arnold.

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