The space structure near a blow-up point for semilinear heat equations: A formal approach (Q1176930)

The authors study the blow-up of a positive solution \(u\) to the parabolic equation \(u_ t-u_{xx}=f(u)\), \(-\infty<x<+\infty\), \(t>0\), where either \(f(u)=\exp u\) or \(f(u)=u^ p\) \((p>1)\). The solution \(u\) is assumed to have a single-point blow-up at \(x=0\) and \(t=T\). By means of formal expansions, a description of \(u\) near the blow-up point is proposed.