Existence of blow-up self-similar solutions for the supercritical
quasilinear reaction-diffusion equation
Existence of blow-up self-similar solutions for the supercritical
quasilinear reaction-diffusion equation
We establish the existence of self-similar solutions presenting finite time blow-up to the quasilinear reaction-diffusion equation $$ u_t=\Delta u^m + u^p, $$ posed in dimension $N\geq3$, $m>1$. More precisely, we show that there is always at least one solution in backward self-similar form if $p>p_s=m(N+2)/(N-2)$. In particular, this establishes \emph{non-optimality …