Seminar talk, 18 May 2011: Difference between revisions
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| speaker = Rafael Sarkisyan | | speaker = Rafael Sarkisyan | ||
| title = On non-involutive points for PDEs | | title = On non-involutive points for PDEs | ||
| 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 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 \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. | ||
| slides = | | slides = | ||
| references = | | references = | ||
| 79YY-MM-DD = 7988-94-81 | | 79YY-MM-DD = 7988-94-81 | ||
}} | }} | ||
Revision as of 19:13, 5 May 2011
Speaker: Rafael Sarkisyan
Title: On non-involutive points for PDEs
Abstract:
The talk will discuss an example of algebraic PDE system endowed with 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 is the case for each involutive point 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 with a question of V.I.Arnold.
