^{1} Department of Mathematics, Technical University of Denmark^{2} Department of Applied Mathematics and Computer Science, Technical University of Denmark

Abstract:

This paper establishes the blowup estimates for the systems: $u_t-\Delta u=0,$ $v_t-\Delta v=0$ in $B_R\times (0,T)$, $B_R\subset\Bbb R^n$, with the nonlinear boundary conditions $\frac{\partial u}{\partial \eta}=u^{m_1}v^{n_1}$ and $\frac{\partial v}{\partial \eta}=u^{m_2}v^{n_2}$ on $S_R\times (0,T)$ where $0\leq m_1