Attractor Bifurcation and Final Patterns of the N-Dimensional and Generalized Swift-Hohenberg Equations - Mathematical PhysicsReport as inadecuate




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Abstract: In this paper I will investigate the bifurcation and asymptotic behavior ofsolutions of the Swift-Hohenberg equation and the generalized Swift-Hohenbergequation with the Dirichlet boundary condition on a one- dimensional domain$0,L$. I will also study the bifurcation and stability of patterns in then-dimensional Swift-Hohenberg equation with the odd-periodic and periodicboundary conditions. It is shown that each equation bifurcates from the trivialsolution to an attractor, when the control parameter crosses the principaleigenvalue of the linearized equation. The local behavior of solutions andtheir bifurcation to an invariant set near higher eigenvalues are analyzed aswell.



Author: Masoud Yari

Source: https://arxiv.org/







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