Blow-up for a semilinear non-local diffusion system. (December 2019) - Ferreira, Raúl
Abstract: In this paper we study the blow-up phenomena for the system u t = ∫ Ω J ( x − y ) u ( y ) d y − u + u α v p ( x, t ) ∈ Ω × ( 0, T ) v t = ∫ Ω J ( x − y ) v ( y ) d y − v + u q v β ( x, t ) ∈ Ω × ( 0, T ) Under certain hypothesis we prove that the solution blows up infinite time and we classify in terms of the parameters when both components blow up together (simultaneous blow-up), or when only one component blows up (non-simultaneous blow-up). We also prove the blow-up rate for a particular case.