Abstract :
Formulas of explicit quadratic Liapunov functions for showing asymptotic stability of the system of
linear partial differential equations ∂u
∂t = A u(t, x) on (0,∞) × Ω, are constructed, where A is an n × n
real matrix, u = (u1,u2, . . . , un)T ,Ω is a bounded domain in Rk with smooth boundary ∂Ω, 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.
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