Singularities and blow-up in viscous Hamilton-Jacobi equations. Lecture 2

I will present some problems related to the occurrence/appearance of singularities in viscous Hamilton-Jacobi equations with coercive superlinear first order terms, in both stationary and time-dependent equations. The main focus will be on boundary blow-up solutions and barrier type phenomena, which have a substantial role in the formation of singularities of time-dependent classical solutions.