Journal ArticleDOI
Path integral synthesis of lyapunov functionals for partial differential equations
Carmine Golia,Jacob M. Abel +1 more
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In this article, a method for constructing Lyapunov functionals for dynamical systems governed by partial differential equations is presented, where the functionals are obtained as path integrals in a suitably chosen state space of a generalized gradient operator.Abstract:
A method is given for constructing Lyapunov Functionals for dynamical systems governed by partial differential equations. The functionals are obtained as path integrals in a suitably chosen state space of a generalized gradient operator, and the method may be viewed as an extension to infinite dimensional systems of the variable gradient technique. Some of the fundamental concepts underlying the formalism are reviewed, and examples of applications to some linear, non-linear and hybrid systems are given.read more
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Stability and uniqueness for a turbulence model of Burgers
Journal ArticleDOI
Stability and bifurcation in a modulated Burgers system
W. E. Olmstead,Stephen H. Davis +1 more
TL;DR: In this paper, the stability of the null state for a nonlinear Burgers system is examined and an energy estimate for global stability for states involving arbitrary modulation in time is provided.
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Stability of a viscoelastic burgers flow
TL;DR: In this article, the system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects, and the stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number.
References
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Journal ArticleDOI
The variable gradient method for generating liapunov functions
D. G. Schultz,J. E. Gibson +1 more
TL;DR: In this paper, a logical and systematic method of generating Liapunov functions for determining stability of nonlinear autonomous systems is introduced, based upon the assumption of a variable gradient function from which both V and V may be determined.
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A guide to methods for the generation of liapunov functions
Okan Gurel,Leon Lapidus +1 more
Journal ArticleDOI
Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.
TL;DR: In this article, an approach for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space is presented, where the objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium.