Studying singular solutions of a semilinear heat equation by a dilation rescaling numerical method (Q1176411)

A computational study is made of the behavior near blowup for solutions of the nonlinear heat equation (*) \(\partial_ tu=\Delta u+| u|^{p-1}u\). It is clear that for \(p>1\) the equation (*) has spatially-independent solutions which blow up at the rate \(C/(t_ 0- t)^{1/(p-1)}\) for any positive \(t_ 0\) and for \(C=1/(p-1)^{1/(p- 1)}\). Computations performed on scaled versions of (*) indicate that the same rate of blowup occurs for spike solutions. The computations furthermore indicate the spatial scaling of a spike.