Journal article
Interaction Manifolds for Reaction Diffusion Equations in Two Dimensions
SIAM journal on applied dynamical systems, v 9(3), pp 734-768
01 Jan 2010
Abstract
We consider a general planar reaction diffusion equation which we hypothesize has a localized traveling wave solution. Under assumptions which are no stronger than those needed to prove the stability of a single pulse, we prove that the PDE has solutions which are roughly the linear superposition of two pulses, so long as they move along trajectories which are not parallel. In particular, we prove that if the initial data for the equation is close to the sum of two separated pulses, then the solution converges exponentially fast to such a superposition so long as the distance between the two pulses remains sufficiently large.
Metrics
Details
- Title
- Interaction Manifolds for Reaction Diffusion Equations in Two Dimensions
- Creators
- J. Douglas Wright
- Publication Details
- SIAM journal on applied dynamical systems, v 9(3), pp 734-768
- Publisher
- Siam Publications
- Number of pages
- 35
- Grant note
- DMS 0807738 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000285549800003
- Scopus ID
- 2-s2.0-77958045090
- Other Identifier
- 991019174512804721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical