Abstract
Symmetry and symmetry-breaking are features widely involved in nonlinear phenomena in nature and science. Reaction-diffusion equations have rich underlying symmetries, which origins, e.g., from the Euclidean symmetry of the Laplace operator. The continuous symmetry of a differential operator is often subjected to symmetries of domains, boundary conditions and reaction terms. We observe it normally in a discrete form. But its existence as underlying symmetries has profound impact on behavior of the system. Symmetries often induce multiple bifurcations and sophisticated scenarios in solution manifolds. For examples, symmetry-breaking, symmetry-increasing and twist of spatial and temporal symmetries are typical bifurcations in pattern formation of reaction-diffusion problems.
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© 2000 Springer-Verlag Berlin Heidelberg
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Mei, Z. (2000). Bifurcation Problems with Symmetry. In: Numerical Bifurcation Analysis for Reaction-Diffusion Equations. Springer Series in Computational Mathematics, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04177-2_5
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DOI: https://doi.org/10.1007/978-3-662-04177-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08669-4
Online ISBN: 978-3-662-04177-2
eBook Packages: Springer Book Archive