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Conservation laws and Euler operators

Presented by: 
Peter Hydon
Wednesday 11th September 2019 - 14:00 to 15:00
INI Seminar Room 2
A (local) conservation law of a given system of differential or difference equations is a divergence expression that is zero on all solutions. The Euler operator is a powerful tool in the formal theory of conservation laws that enables key results to be proved simply, including several generalizations of Noether's theorems.  This talk begins with a short survey of the main ideas and results.   The current method for inverting the divergence operator generates many unnecessary terms by integrating in all directions simultaneously. As a result, symbolic algebra packages create over-complicated representations of conservation laws, making it difficult to obtain efficient conservative finite difference approximations symbolically. A new approach resolves this problem by using partial Euler operators to construct near-optimal representations. The talk explains this approach, which was developed during the GCS programme.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons