On new exact blow-up solutions for nonlinear heat conduction equations with source and applications (Q1174355)

The author considers five classes of quasilinear parabolic equations describing nonlinear heat conduction with source, of the type \(u_ t=\Delta\varphi(u)+Q(u)\), and presents a method of constructing new exact solutions for these equations. Moreover, some applications are given regarding localization properties of blow-up solutions for two of these equations, namely \[ u_ t=(| u_ x| u_ x)_ x+u^ 2,\quad u_ t=(u^ \sigma u_ x)_ x+u^{\sigma+1}. \]