Stationary patterns for anadsorbate-induced phase transition model I: Existence
Kousuke Kuto, Tohru Tsujikawa · Discrete and Continuous Dynamical Systems - B · 2010
We are concerned with a reaction-diffusion-advection system proposed byHildebrand [4].This system isa phase transition model arising insurface chemistry.For this model,several stationary patterns have been shownby 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-Schauderdegree theory.Some a priori estimates for solutions play animportant role in the proof.