Critical Non-simultaneous Blow-up Exponents for a Reaction-diffusion System
Bingchen Liu, Fengjie Li, Sining Zheng · Advances in Mathematics · 2011
The paper deals with the critical non-simultaneous blow-up exponents for the coupled reaction-diffusion equations ut =Δ u + u m v p and vt =Δ v + u q v n , subject to homo- geneous Dirichlet boundary conditions. For the radial blow-up solutions, we propose precise criteria to completely identify the four cases for non-simultaneous and simultaneous blow-up situations under admissible initial data: there exist initial data such that non-simultaneous (or simultaneous) blow-up of solutions occurs, or any blow-up must be non-simultaneous (or simultaneous). The necessary-sufficient conditions are established for each case with a complete classification for all the parameters there. Moreover, all possible simultaneous blow-up rates are obtained. These extend the results in the previous works for the same model.