On global existence for the Gierer-Meinhardt system

Academic Article

Abstract

  • We consider the Gierer-Meinhardt system (1.1), shown below, on a bounded smooth domain Ω ⊂ Rn(n ≥ 1) with a homogeneous Neumann boundary condition. For suitable exponents a, b, c and d, we establish certain sufficient conditions for global existence. Theorem 1.1 here, combined with Theorem 1.2 of [6], implies a classical phenomenon on the effect of the initial data on global existence and finite time blow-up. This work is a continuation of our earlier result [6] for the Gierer-Meinhardt system. The Gierer-Meinhardt system was introduced in [1] to model activator-inhibitor systems in pattern formation in ecological systems.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Zou H
  • Start Page

  • 583
  • End Page

  • 591
  • Volume

  • 35
  • Issue

  • 1