Blow-up at the boundary for degenerate semilinear parabolic equations

This paper treats a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover, it is proved that for a large class of initial data, blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The mathematical analysis is then extended to equations with other degeneracies.