English

Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions

Analysis of PDEs 2010-11-16 v1

Abstract

The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator-prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.

Keywords

Cite

@article{arxiv.1011.3334,
  title  = {Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions},
  author = {Christoph Walker},
  journal= {arXiv preprint arXiv:1011.3334},
  year   = {2010}
}