Abstract
Stability study of stationary solutions of the viscous Burgers equation using Fourier mode stability analysis for the stationary solutions , where is constant and , in two cases is analyzed. Firstly when the wave amplitude is constant and secondly when the wave amplitude is variable. In the case of constant amplitude, the results found to be: The solution is always stable while the solution is conditionally stable. In the case of variable amplitude, it has been found that the solutions and are conditionally stable.
Highlights
Consider a system of any nature whatsoever that exists in a state S.We say that S is stable, in one sense or another, if small perturbations or changes in the system do not drastically affect the state S
It is known that if a small additional celestial body is introduced into the system, the original state is not disturbed to any significant degree
We say that the original state is stable to small perturbations
Summary
Consider a system of any nature whatsoever that exists in a state S. Burns et al [8] considered the numerical stationary solutions for a viscous Burgers equation on the interval (0,1) with Neumann boundary conditions. Balogh et al [5] studied the stationary solutions of a one–parameter family of boundary control problems for a forced viscous Burgers equation. They assumed that the forcing term possesses a special symmetry. Moller [23] studied and conducted some numerical experiments on the 1D viscous Burgers equation in linear and nonlinear cases with the same stationary solution. The stability of stationary solutions of viscous Burgers equation using Fourier mode stability analysis is investigated
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