In this talk I will give an overview on dynamic blocking problems of
Fire Propagation with a particular focus on Bressan Fire Conjecture,
proposed in 2007. It is concerned with the model of wild fire
spreading in a region of the plane $\mathbb{R}^2$ and the possibility
to block the fire surrounding it with barriers (strategies)
constructed in real time. I will talk about recent advancements on
the topic and I will discuss some new ideas that help to determine
the shape of the optimal strategy without requiring any regularity
result on the barrier, differently from what was previously
done. Optimal strategies are those ones with minimum length that
minimize the area burned by the fire . This set of tools gave us the
possibility to examine concretely some few cases, in which we could
prove that Bressan Conjecture is true.
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