Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem
Philippe Souplet, Juan-Luis V aacute zquez · Discrete and Continuous Dynamical Systems · 2006
This paper is devoted to analyze a case of singularity formationin infinite time for a semilinear heat equation involving lineardiffusion and superlinear convection. A feature to be noted isthat blow-up happens not for the main unknown but for itsderivative. The singularity builds up at the boundary. Theformation of inner and outer regions is examined, as well as thematching between them. As a consequence, we obtain the preciseexponential rates of blow-up in infinite time.