Two-Sided Estimates of Solutions with a Blow-Up Mode for a Nonlinear Heat Equation with a Quadratic Source

We study compactly supported solutions $u(x, t) \geqslant 0$, $x \in \mathbb{R}$, $t \geqslant 0$, to a one-dimensional quasilinear heat transfer equation degenerating for $u(x, t)=0$. The equation has a $u$-linear transport coefficient and a self-consistent source $\alpha u+\beta u^{2}$ of general form. For the blow-up time of compactly supported solutions we establish two-sided estimates depending functionally on the initial conditions $u(x, 0)$.