Rayleigh-Bénard Convection, Dynamic Bifurcation And Stability
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Abstract
In this paper, we look at the bifurcation and stability of Boussinesq equation solutions, as well as the onset of Rayleigh- Bnard convection. nonlinear theory,was developed based on a new concept of bifurcation called attractor bifurcation and its corresponding theorem . The three aspects of this principle are as follows. First, regardless of the multiplicity of the eigenvalue for the linear problem, the problem bifurcates from the trivial solution attractor when the Rayleigh number exceeds the first critical Rayleigh number for all physically sound boundary conditions. Second, the asymptotically stable bifurcated attractor . Third, bifurcated solutions are structurally stable and can be classified when the spatial dimension is two. Furthermore, the technical approach developed offers a recipe that can be used to solve a variety of other bifurcation and pattern forming problems.
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