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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The dynamics of rotating waves in scalar reaction diffusion equations
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by S. B. Angenent and B. Fiedler PDF
Trans. Amer. Math. Soc. 307 (1988), 545-568 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • 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