Blow-up and quenching for solutions of some parabolic equations.

摘要

This dissertation consists of four problems concerning blow-up and quenching phenomena for solutions of some parabolic equations. The first and second ones are related to heat diffusion models with presence of two nonlinearities, one in the equation and the other in the boundary, for which we establish results for finite time blow-up and quenching, blow-up and quenching rates, and blow-up and quenching sets. The third one under consideration is a parabolic system coupled in an equation and a boundary condition on a bounded domain, where we give a global existence and global nonexistence result and localize the blow-up points. The fourth one being considered is an investigation of the steady-states of the second problem, where we obtain bifurcation diagrams for the positive solutions of the stationary problem.