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Index theory for traveling waves in reaction diffusion systems with skew gradient structure.
- Source :
- Proceedings of the American Mathematical Society; Jul2021, Vol. 149 Issue 7, p2891-2909, 19p
- Publication Year :
- 2021
-
Abstract
- A unified geometric approach for the stability analysis of traveling pulse solutions for reaction diffusion equations with skew-gradient structure has been established in a previous paper (see Paul Cornwell [Indiana Univ. Math. J. 68 (2019), pp. 1801-1832]), but essentially no results have been found in the case of traveling front solutions. In this work, we will bridge this gap. For such cases, a Maslov index of the traveling wave is well-defined, and we will show how it can be used to provide the spectral information of the waves. As an application, we use the same index providing the exact number of unstable eigenvalues of the traveling front solutions of FitzHugh-Nagumo equations. [ABSTRACT FROM AUTHOR]
- Subjects :
- HEAT equation
GEOMETRIC approach
REACTION-diffusion equations
EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 150284284
- Full Text :
- https://doi.org/10.1090/proc/15398