Global existence and blowup solutions for the Gierer–Meinhardt system. (July 2020) - Chen, Shaohua; Melnick, Brittney; Xu, Runzhang
Abstract: We discuss global and blowup solutions for general Gierer–Meinhardt system with zero Neumann boundary conditions, which originally arose in studies of pattern-formation in biology and has interesting and challenging mathematical properties. We obtain some new sufficient conditions for global existence and finite time blow-up of solutions. In some special cases, the results are sharp.