Solutions of the Boussinesq Equations Through Bifurcation Method

Authors

  • Mohammad Yahia Ibrahim Awajan, Ruwaidiah Idris

DOI:

https://doi.org/10.17762/msea.v72i1.1613

Abstract

The article established the nonlinear theory to find the solution using a new notion of bifurcation known as attractor bifurcation. It determined the bifurcation and stability of the solutions of the Boussinesq equations as well as the onset of the Rayleigh-Benard convection. In this article we considered the theory that comprises the succeeding perspectives. The study initially deal with the problem that bifurcates from the trivial solution an attractor A_R while the Rayleigh number R intersects the ?rst critical Rayleigh number R_C for all physically boundary conditions, despite the multiplicity of the eigenvalue R_C for the linear problem. Hereafter, secondly, the study measured the bifurcated attractor A_R as asymptotically stable. Finally, the bifurcated solutions are also structurally stable when the spatial dimension is two, and are classi?ed as a bifurcated solution as well. Furthermore, the technical method explained here provides a means, which can be adopted for many differen.

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Published

2023-01-13

How to Cite

Mohammad Yahia Ibrahim Awajan, Ruwaidiah Idris. (2023). Solutions of the Boussinesq Equations Through Bifurcation Method. Mathematical Statistician and Engineering Applications, 72(1), 12–28. https://doi.org/10.17762/msea.v72i1.1613

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Articles