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A Group‐Theoretic Approach to Parameter Identifiability of PDE Systems
Author(s) -
Rieger Karl,
Schlacher Kurt
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010302
Subject(s) - identifiability , group (periodic table) , coordinate system , nonlinear system , mathematics , transformation (genetics) , boundary (topology) , boundary value problem , lie group , trajectory , mathematical optimization , mathematical analysis , pure mathematics , physics , geometry , statistics , chemistry , quantum mechanics , astronomy , biochemistry , gene
The contribution is devoted to the parameter identifiability problem of (nonlinear) PDE systems. Especially, we discuss the (local) identifiability of parameters along a trajectory. The analysis relies on a coordinate‐free formulation for systems, including boundary conditions, and we motivate an approach by (Lie) transformation groups, whose success for PDE systems depends on a consequent extent to the accompanying boundary conditions. The (non‐)identifiability of parameters is related to the (non‐)existence of group generators, wherewith (local) conditions can be derived. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)