Abstract
In this paper, an adaptive numerical method is proposed to solvethe Gierer-Meinhardt (GM) system on irregular domain. The methodworks for domains defined by level sets of implicit functions andthe generated mesh is of high quality. The method is shown to beeffective by comparing with asymptotic result. Boundary spikesolutions of the GM system are obtained and studied numerically,including stability of boundary spike and spike motion along theboundary.
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