Formulas of Liapunov functions for systems of linear partial differential equations
Document Type
Article
Publication Date
1-15-2007
Abstract
Formulas of explicit quadratic Liapunov functions for showing asymptotic stability of the system of linear partial differential equations frac(? u, ? t) = A ? u (t, x) on (0, ?) × ?, are constructed, where A is an n × n real matrix, u = (u1, u2, ..., un)T, ? is a bounded domain in Rk with smooth boundary ??, and ? denotes the Laplacian operator on Rk with ? u = (? u1, ? u2, ..., ? un)T. These formulas are also modified and applied to a number of nonautonomous linear and nonlinear systems and models in structural stability, traveling wave, and Navier-Stokes equations. © 2006 Elsevier Inc. All rights reserved.
Recommended Citation
Zhang, Bo, "Formulas of Liapunov functions for systems of linear partial differential equations" (2007). College of Health, Science, and Technology. 103.
https://digitalcommons.uncfsu.edu/college_health_science_technology/103