A note on blow-up of a nonlinear integral equation

Blow up of mild solutions of a system of partial differential equations with distinct fractional diffusions

“…Also, from this we see that C V , given in (12), is not the optimal bound (critical dimension), but we believe that it is the best we can get by constructing a convenient subsolution of the solution of (2). In fact, the condition (8) coincides with the condition for blow up given by Pérez and Villa [11].…”

“…, Fujita [3] showed that if d < α 1 /β 1 , then for any non-vanishing initial condition the solution of ( 9) is infinite for all t large enough. 9), Pérez and Villa [11] showed that if σ 1 + 1 ≥ dρ 1 (β 1 − 1)/α 1 , then the solutions of (9) blow up in finite time.…”

“…When α 1 = α 2 = 2, ρ 1 = ρ 2 = 1 and σ 1 = σ 2 = 0 the Uda condition (10), the Pérez condition (11) and the condition (8) become…”

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

“…The cases where A = −(−∆) α 2 is the fractional power of the Laplacian, 0 < α < 2, have been used in models of anomalous growth of certain fractal interfaces [16]. The articles [3,15,18,20,27,32,33,34] are only a few examples for the study of global existence and blow up in finite time of positive solutions.…”