Blow-up for a heat equation with convection and boundary flux
Arturo de Pablo, Guillermo Reyes, Ariel Sánchez · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2008
We study the evolution of solutions to the initial-boundary-value problem\begin{alignat*}{3} u_t&=(u^m)_{xx}+\lambda(u^q)_x, & \quad x&>0,&\quad t&\in(0,T), \\[2pt] -(u^m)_x(0,t)&=u^p(0,t), & &&t&\in(0,T), \\[2pt] u(x,0)&=u_0(x), & \quad x&>0, \end{alignat*}and give a rather complete characterization, in terms of the parameters .