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Local Decompositions of Second Order Infinite‐Dimensional Systems
Author(s) -
Rams Hubert,
Schöberl Markus,
Schlacher Kurt
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610401
Subject(s) - decomposition , nonlinear system , simple (philosophy) , mathematics , partial differential equation , order (exchange) , boundary (topology) , vector field , field (mathematics) , first order , differential (mechanical device) , mathematical analysis , pure mathematics , geometry , physics , ecology , philosophy , epistemology , finance , quantum mechanics , economics , biology , thermodynamics
This article deals with the local system decomposition of infinite‐dimensional systems, which are described by second‐order nonlinear partial differential equations. It will be shown that the existence of a certain codistribution allows a local triangular decomposition of the generalized system vector field and the boundary conditions. Based on this triangular decomposition, non‐accessibility follows by a simple structural analysis. Throughout the article differential geometric methods are applied, highlighting the geometric picture behind the system description. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)