Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system

In this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion solution following non-local problem: [Formula: see text] where is bounded domain in with smooth boundary such problem derived as shadow limit singular Gierer–Meinhardt system, Kavallaris and Suzuki [On dynamics parabolic equation arising from Nonlinearity (2017) 1734–1761; Non-Local Partial Differential Equations for Engineering Biology: Mathematical Modeling Analysis, Mathematics Industry, Vol. 31 (Springer, 2018)]. Under Turing type condition construct which blows finite time only at an interior point i.e. More precisely, also give description on final asymptotic profile blowup thus unveil form patterns occurring that case due to driven-diffusion instability. The applied technique construction preceding mainly relies approach developed [F. Merle H. Zaag, Reconnection vortex quenching, 10 (1997) 1497–1550] [G. K. Duong Profile touch-down nonlocal MEMS model, Math. Models Methods Appl. Sci. 29 (2019) 1279–1348].