A flame propagation model on a network with application to a blocking problem

Fabio Camilli; Elisabetta Carlini; Claudio Marchi

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arXiv · 1411.3260

A flame propagation model on a network with application to a blocking problem

Fabio Camilli·Elisabetta Carlini·Claudio Marchi

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Abstract

We consider the Cauchy problem \[\partial_t u+H(x,Du)=0 \quad (x,t)\in\Gamma\times (0,T),\quad u(x,0)=u_0(x) \quad x\in\Gamma\] where $\Gamma$ is a network and $H$ is a convex and positive homogeneous Hamiltonian which may change from edge to edge. In the former part of the paper, we prove that the Hopf-Lax type formula gives the (unique) viscosity solution of the problem. In the latter part of the paper we study a flame propagation model in a network and an optimal strategy to block a fire breaking up in some part of a pipeline; some numerical simulations are provided.

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BibTeX RIS

Fabio Camilli, Elisabetta Carlini, Claudio Marchi. 2014-11-12. A flame propagation model on a network with application to a blocking problem. https://arxiv.org/abs/1411.3260

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