| Contents |
| In this talk, we discuss the local (in time) solvability and the finite time blow-up of positive solutions for the Cauchy-Neumann problem in a bounded domain $\Omega$ of $\mathbb R^N$ for a fully nonlinear parabolic equation involving a "positive part function" $(x)_+ := x \vee 0$ for $x \in \mathbb R$,
$$
\partial_t u = g(u) \left( \lambda \Delta u + u \right)_+ \quad \mbox{ in } \Omega \times (0,+\infty),
$$
where $g(u)$ is a positive function and $\lambda > 0$. |
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