Pattern formations in two-dimensional Gray-Scott model: existence of single-spot solutions and their stability

摘要

The Gray-Scott model has been studied extensively in recent years. However, most of the results are in one dimension. In this paper, we study the 2D Gray-Scott system. We first construct two single-spot solutions and then we establish the stability and instability of such solutions in terms of the parameters involved. (C) 2001 Published by Elsevier Science B.V. MSC: 35K57: 35J40: 35B10. [References: 49]