Stationary patterns for an adsorbate-induced phase transition model I: Existence

Kousuke Kuto, Tohru Tsujikawa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We are concerned with a reaction-diffusion-advection system proposed by Hildebrand [4]. This system is a phase transition model arising in surface chemistry. For this model, several stationary patterns have been shown by the numerical simulations (e.g., [15]). In the present paper, we obtain sufficient conditions for the existence (or nonexistence) of nonconstant stationary solutions. Our proof is based on the Leray-Schauder degree theory. Some a priori estimates for solutions play an important role in the proof.

Original languageEnglish
Pages (from-to)1105-1117
Number of pages13
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume14
Issue number3
DOIs
Publication statusPublished - 2010 Oct 1
Externally publishedYes

Keywords

  • A priori estimate
  • Advection
  • Degree theory
  • Reaction-diffusion
  • Stationary pattern

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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