Complete and Incomplete Blow-up in Several Space Dimensions
Victor A. Galaktionov · 2004
In this chapter we apply intersection comparison techniques to the study of complete and incomplete blow-up phenomena for quasilinear heat equations in . First we present a detailed construction of limit semigroups of minimal solutions to quasilinear heat equations admitting finite-time blow-up. Second we show that, in the complete-incomplete blow-up phenomena in , a crucial role is played by the critical Sobolev exponent for the elliptic operator of the reactiondiffusion equation under consideration. The results are extended to another singular phenomenon of finite-time extinction for equations with absorption.