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Transactions of the American Mathematical Society

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

 
 

 

Infinitely many traveling wave solutions of a gradient system


Author: David Terman
Journal: Trans. Amer. Math. Soc. 301 (1987), 537-556
MSC: Primary 35K55; Secondary 35B99
DOI: https://doi.org/10.1090/S0002-9947-1987-0882703-6
MathSciNet review: 882703
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Abstract: We consider a system of equations of the form $ {u_t} = {u_{xx}} + \nabla F(u)$. A traveling wave solution of this system is one of the form $ u(x,\,t) = U(z),\,z = x + \theta t$. Sufficient conditions on $ F(u)$ are given to guarantee the existence of infinitely many traveling wave solutions.


References [Enhancements On Off] (What's this?)

  • [1] C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math., no. 38, Amer. Math. Soc., Providence, R. I., 1978. MR 511133 (80c:58009)
  • [2] P. Hartman, Ordinary differential equations, 2nd ed, Birkhauser, Boston, Mass., 1982. MR 658490 (83e:34002)
  • [3] D. Terman, Directed graphs and traveling waves, Trans. Amer. Math. Soc. 289 (1985), 809-847. MR 784015 (86e:35072)
  • [4] -, Infinitely many radial solutions of an elliptic system (submitted).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0882703-6
Article copyright: © Copyright 1987 American Mathematical Society

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