Decomposition Invariance of Generalized Steady-State of a 1-D Diffusion System

摘要

Decomposition invariance of the generalized steady state is elucidated for a 1-D (one dimensional) diffusion system. The boundary conditions are conceived to be corner input signals forcing the so called 'generalized steady state' solution upon the diffusion system. The discussion is based upon the use of the mathematical formulation of this system concept as an infinite series expansion of the derivatives of the corner inputs signals. For large scale systems the 'generalized steady state' is often the main part of the state. Computer simulation of large systems requires partitioning of the definition region into (many) small regions. Then application of the concept generalized steady state only makes sense if the generalized steady state is invariant under spatial decomposition. It is demonstrated that the generalized steady state of a 1-D diffusion system is decomposition invariant by nature.