We consider the Cauchy problem (Equation Presented) where - is a network and H is a positive homogeneous Hamiltonian which may change from edge to edge. In the first 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 ame 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.
A flame propagation model on a network with application to a blocking problem / Camilli, Fabio; Carlini, Elisabetta; Marchi, Claudio. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 11:5(2018), pp. 825-843. [10.3934/dcdss.2018051]
A flame propagation model on a network with application to a blocking problem
Camilli, Fabio;Carlini, Elisabetta;Marchi, Claudio
2018
Abstract
We consider the Cauchy problem (Equation Presented) where - is a network and H is a positive homogeneous Hamiltonian which may change from edge to edge. In the first 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 ame 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.| File | Dimensione | Formato | |
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Camilli_Flame-propagation_2018.pdf
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