Point-condensation for a reaction-diffusion system

Izumi Takagi

Research output: Contribution to journalArticlepeer-review

108 Citations (Scopus)


We consider stationary solutions of a reaction-diffusion system for an activator and an inhibitor. Let d1 and d2 be the respective diffusion coefficients of the activator and the inhibitor. Assuming that d2 is sufficiently large, we construct stationary solutions which exhibit spiky patterns when d1 is near zero. Moreover, we study the global (in d1) structure of the solution set and show that if d2 is sufficiently large then (a) whenever bifurcation from the constant solution occurs, there exists a continuum of nonconstant solutions which connects the point-condensation solutions with the bifurcating solutions; and (b) when no bifurcation from the constant solution occurs, the point-condensation solutions are connected to another family of point-condensation solutions.

Original languageEnglish
Pages (from-to)208-249
Number of pages42
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 1986 Feb

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Point-condensation for a reaction-diffusion system'. Together they form a unique fingerprint.

Cite this