Single-point blow-up on the boundary where the zero Dirichlet boundary condition is imposed

Abstract

We consider a reaction-diffusion-convection equation on the halfline $(0,\infty )$ with the zero Dirichlet boundary condition at $x=0$. We find a positive selfsimilar solution $u$ which blows up in a finite time $T$ at $x=0$ while $u(x,T)$ remains bounded for $x>0$.