Existence, stability and metastability of point condensation patterns generated by the Gray-Scott system

Of concern are point condensation patterns in the generalized Gray-Scott mo del in the higher-dimensional case. We first establish the existence of bou ndary condensation or interior condensation under some assumptions on the g eometry of the domain. Then we study the stability of such patterns. It tur ns out the stability of point condensations depends on three factors: the d omain geometry, the boundary conditions and the exponents in the reaction t erms. We also classify the instability and metastability of point condensat ions.