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The dynamics of rotating waves in scalar reaction diffusion equations


Authors: S. B. Angenent and B. Fiedler
Journal: Trans. Amer. Math. Soc. 307 (1988), 545-568
MSC: Primary 35K57; Secondary 58F12
DOI: https://doi.org/10.1090/S0002-9947-1988-0940217-X
MathSciNet review: 940217
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Abstract: The maximal compact attractor for the RDE $ {u_t} = {u_{xx}} + f(u,\,{u_x})$ with periodic boundary conditions is studied. It is shown that any $ \omega $-limit set contains a rotating wave, i.e., a solution of the form $ U(x - ct)$. A number of heteroclinic orbits from one rotating wave to another are constructed. Our main tool is the Nickel-Matano-Henry zero number. The heteroclinic orbits are obtained via a shooting argument, which relies on a generalized Borsuk-Ulam theorem.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0940217-X
Article copyright: © Copyright 1988 American Mathematical Society

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