β Scribed by Y.H. Lin; E. Kinnen; J.C. Friedly
No coin nor oath required. For personal study only.
Stability theorems for distributed parameter dynamical systems are stated in terms of exterior differential forms. It is shown that these n-forms can be used to develop a relatively systematic procedure for constructing Liapunov functionals. The procedure is demonstrated on linear and nonlinear slab catalyst stability problems, including Lef 1. The examples illustrate several advantages of the construction procedure. Nonquadratic Liapunov functionals can be developed for nonlinear problems. Systematic corrections to the functionals follow directly from the construction procedure. The technique is applicable to both single and systems of partial differential equations. Numerical calculations are presented showing that improvements up to I-fold can be realized by starting with previously published results and generating corrections using the formalism of exterior differential forms.
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