Large Stable Pulse Solutions in Reaction-di ff usion Equations

@inproceedings{Gardner2000LargeSP,
  title={Large Stable Pulse Solutions in Reaction-di ff usion Equations},
  author={Robert A. Gardner and Tasso J. Kaper},
  year={2000}
}
In this paper we study the existence and stability of asymptotically large stationary multi-pulse solutions in a family of singularly perturbed reaction-diffusion equations. This family includes the generalized Gierer-Meinhardt equation. The existence of N-pulse homoclinic orbits (N ≥ 1) is established by the methods of geometric singular perturbation theory. A theory, called the NLEP (=NonLocal Eigenvalue Problem) approach, is developed, by which the stability of these patterns can be studied… CONTINUE READING