Special Session 77: Singularity and regularity in nonlinear PDEs

Fujita`s critical exponent for Fractional Reaction-Diffusion Systems on $\mathbb{R}^{N}$
Soon-Yeong Chung
Sogang University, Seoul
Korea
Co-Author(s):    Soon-Yeong Chung
Abstract:
In this talk, we are going to introduce Fujita`s critical exponent to determine whether a fractional reaction-diffusion system (S) admits a global solutions or only blow-up solutions. In fact, the number $(pq)^{*}$ is introduced as the critical exponent to prove
i If $(pq)^* < pq$, then (S) has a global solution for some initial data.
ii If $(pq)^* \geq pq$, then every nontrivial and non-negative solution to (S) blows up in finite time.