On diffusion-induced blowups in a mutualistic model (Q5940138)

The authors study the effect of diffusion on the blowup of solutions of the semilinear parabolic system NEWLINE\[NEWLINE \begin{aligned} u_t=d_1\Delta u+u(a_1-b_1u+c_1v) &\quad \text{in} \Omega\times(0,T^*),\\ v_t=d_2\Delta v+v(a_2-b_2u-c_2v) &\quad \text{in} \Omega\times(0,T^*),\\ \partial u/\partial\nu=\partial v/\partial\nu=0 &\quad \text{on} \partial\Omega\times(0,T^*),\\ u(x,0)=u_0(x),\;v(x,0)=v_0(x) &\quad \text{in} \overline\Omega,\end{aligned} NEWLINE\]NEWLINE with a bounded and smooth domain \(\Omega\subset{\mathbb R}^n\) and \(T^*\) being the maximal existence time of the solution.