Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 055, 9 pages      arXiv:1106.1495      https://doi.org/10.3842/SIGMA.2011.055
Contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”

Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics

Yuri Bozhkov a and Peter J. Olver b
a) Instituto de Matemática, Estatistica e Computação Científica - IMECC, Universidade Estadual de Campinas - UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859 - Campinas - SP, Brasil
b) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Received February 01, 2011, in final form June 02, 2011; Published online June 08, 2011

Abstract
We construct identities of Pohozhaev type, in the context of elastostatics and elastodynamics, by using the Noetherian approach. As an application, a non-existence result for forced semi-linear isotropic and anisotropic elastic systems is established.

Key words: Pohozhaev identity; Navier's equations; Noether's theorem.

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