This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under ce...This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.展开更多
文摘This paper deals with the blow-up properties of solutions to the systems ut=Δu,vt=Δv in BR × (O,T) subject to nonlinear boundary conditions δu/δη=v^p,δu/δη=u^q, in SR×(O,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived.
