Dynamical Bifurcation of the Burgers-Fisher equation

Yuncherl Choi

Abstract


In this paper, we study dynamical Bifurcation of  the Burgers-Fisher equation. We show that the equation bifurcates an invariant set $\mathcal{A}_n (\beta)$ as the control parameter $\beta$ crosses over $n^2$ with $n \in \mathbb{N}$. It turns out that  $\mathcal{A}_n (\beta)$  is homeomorphic to $S^1$, the unit circle.


Keywords


Burgers-Fisher equation; dynamic bifurcation; center manifold

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References


H. Berestycki, S. Kamin and G. Sivashinsky, Metastability in a flame front evolution equation, Interfaces and Free Boundaries, 3 (2001), 361–392.

Y. Choi, Dynamical bifurcation of the one-dimensional convective Cahn-Hilliard equation, Korean J. Math. 22 (2014), 621–632.

C.-H. Hsia and X. Wang, On a Burgers’ type equation, Dics. Cont. Dyn. Syst. B 6 (2006), 1121–1139.

J. Logan, An introduction to nonlinear partial differential equations, Pure and Applied Mathematics, John Wiley and Sons Inc., New York, 1994.

L. Mei and K. W. Ong, Dynamic tansition of generalized Burgers equation, J. Math. Fluid Mech. 18 (2016), 89–101.

T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific, 2005.

W. Xinyi and L. Yuekai, Exact solutions of the extended Burgers-Fisher equation, Chinse Phys. Lett. 7 (1990), 145–147.




DOI: http://dx.doi.org/10.11568/kjm.2016.24.4.637

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ISSN: 1976-8605 (Print), 2288-1433 (Online)

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