Blow-up results for a reaction-diffusion system (Q937849)

The author considered the Cauchy problem for the reaction-diffusion system with the nonlinear terms \(|x|^{\sigma_j}u^{p_j}v^{q_j}\). It is shown that the exponents \(p_j , q_j , \sigma_j\) play a crucial role to determine the behavior of the solutions. Using an ODE method, the author proved the Fujita-type nonexistence results for \(p_1, q_2<1\), for \(q_2<1<p_1\) or for \(p_1, q_2>1\). In addition, the author also showed the nonexistence results for large initial data.