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Symmetry Groups and the Observability of PDEs
Author(s) -
Kolar Bernd,
Schöberl Markus
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800019
Subject(s) - observability , symmetry (geometry) , observable , symmetry group , nonlinear system , mathematics , rotational symmetry , group (periodic table) , differential (mechanical device) , representation (politics) , pure mathematics , global symmetry , symmetry operation , mathematical analysis , physics , symmetry breaking , geometry , spontaneous symmetry breaking , law , quantum mechanics , politics , political science , thermodynamics
Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this contribution, we use symmetry groups for studying the observability of systems of nonlinear PDEs with input and output. Based on a differential‐geometric representation of the system, we present conditions for the existence of special symmetry groups that do not change the trajectories of the input and the output. If such a symmetry group exists, the system cannot be observable.