English

Solutions with peaks for a coagulation-fragmentation equation. Part I: stability of the tails

Analysis of PDEs 2019-06-24 v1

Abstract

The aim of this two-part paper is to investigate the stability properties of a special class of solutions to a coagulation-fragmentation equation. We assume that the coagulation kernel is close to the diagonal kernel, and that the fragmentation kernel is diagonal. We construct a two-parameter family of stationary solutions concentrated in Dirac masses. We carefully study the asymptotic decay of the tails of these solutions, showing that this behaviour is stable. In a companion paper we prove that for initial data which are sufficiently concentrated, the corresponding solutions approach one of these stationary solutions for large times.

Keywords

Cite

@article{arxiv.1906.08965,
  title  = {Solutions with peaks for a coagulation-fragmentation equation. Part I: stability of the tails},
  author = {Marco Bonacini and Barbara Niethammer and Juan Velázquez},
  journal= {arXiv preprint arXiv:1906.08965},
  year   = {2019}
}