A priori estimates of stationary solutions of an activator-inhibitor system

Huiqiang Jiang, Wei Ming Ni

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We consider positive solutions of the stationary Gierer-Meinhardt system d1Δ - u + up/vq + σ = 0 in Ω, d2Δv - + ur/vs = 0 in Ω, ∂u/∂ν = ∂v/∂ν = 0 on ∂Ω where Δ is the Laplace operator, Ω is a bounded smooth domain in ℝn, n ≥ 1, and ν is the unit outer normal to ∂Ω. Under suitable conditions on the exponents p, q, r, and s, different types of a priori estimates are obtained, existence and non-existence results of nontrivial solutions are derived, for both σ > 0 and σ = 0 cases. Indiana University Mathematics Journal

Original languageEnglish (US)
Pages (from-to)681-732
Number of pages52
JournalIndiana University Mathematics Journal
Volume56
Issue number2
DOIs
StatePublished - 2007

Keywords

  • A priori estimate
  • Activator-inhibitor
  • Existence
  • Gierer-meinhardt
  • Reaction-diffusion

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