Blow-up for a degenerate diffusion problem not in divergence form Arturo de PabloRaul FerreiraJulio Rossi 35B4035B3535K65blow-upasymptotic behaviournonlinear boundary conditions We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, $\mathbb{R}_{+} = (0,\infty)$, with a nonlinear boundary condition, \[ \begin{cases} u_t = uu_{xx}, \quad (x,t) \in \mathbb{R}_{+} \times (0,T),\\ -u_{x}(0,t) = u^{p}(0,t), \quad t \in (0,T),\\ u(x,0) = u_0(x), \quad x \in \mathbb{R}_{+},\\ \end{cases} \] with $p$ greater than $0$. We describe, in terms of $p$ and the initial datum, when the solution is global in time and when it blows up in finite time. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time in terms of a self-similar profile. The stationary character of the support is proved both for global solutions and blowing-up solutions. Also we obtain results for the problem in a bounded interval. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2725 10.1512/iumj.2006.55.2725 en Indiana Univ. Math. J. 55 (2006) 955 - 974 state-of-the-art mathematics http://iumj.org/access/