Travelling wave solutions to a gradient system
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- by James F. Reineck PDF
- Trans. Amer. Math. Soc. 307 (1988), 535-544 Request permission
Abstract:
Given a system of reaction-diffusion equations where the nonlinearity is derived from a potential with certain restrictions, we use the Conley index and the connection matrix to show that there is a travelling wave solution connecting the maxima of the potential.References
- Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, vol. 38, American Mathematical Society, Providence, R.I., 1978. MR 511133 R. Franzosa, Index filtrations and connection matrices for partially ordered Morse decompositions, Thesis, Univ. of Wisconsin, Madison, 1984.
- Robert Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. Amer. Math. Soc. 298 (1986), no. 1, 193–213. MR 857439, DOI 10.1090/S0002-9947-1986-0857439-7
- Robert D. Franzosa, The connection matrix theory for Morse decompositions, Trans. Amer. Math. Soc. 311 (1989), no. 2, 561–592. MR 978368, DOI 10.1090/S0002-9947-1989-0978368-7
- James F. Reineck, Connecting orbits in one-parameter families of flows, Ergodic Theory Dynam. Systems 8$^*$ (1988), no. Charles Conley Memorial Issue, 359–374. MR 967644, DOI 10.1017/S0143385700009482
- Dietmar Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1985), no. 1, 1–41. MR 797044, DOI 10.1090/S0002-9947-1985-0797044-3
- David Terman, Infinitely many traveling wave solutions of a gradient system, Trans. Amer. Math. Soc. 301 (1987), no. 2, 537–556. MR 882703, DOI 10.1090/S0002-9947-1987-0882703-6
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 307 (1988), 535-544
- MSC: Primary 35K57; Secondary 58E05
- DOI: https://doi.org/10.1090/S0002-9947-1988-0940216-8
- MathSciNet review: 940216