The profile near blowup time for solutions of diffusion systems coupled with localized nonlinear reactions
Let \(\Omega\) be a smoothly bounded domain in \(\mathbb{R}^N\), \(x_0\in\Omega\) and \(\lambda_1,\lambda_2>0\). The authors establish the blow-up rate for positive solutions of the system \(u_t=\Delta u+\lambda_1e^{v(x_0,t)}\), \(v_t=\Delta v+\lambda_2e^{u(x_0,t)}\), \((x,t)\in\Omega\times(0,T)\), complemented by the homogeneous Dirichlet boundary conditions on \(\partial\Omega\times(0,T)\). They also show that the blow-up is global and they study the asymptotic behavior of solutions near the boundary \(\partial\Omega\).
homogeneous Dirichlet boundary conditions
scientific article; zbMATH DE number 1788053