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A flame propagation model on a network with application to a blocking problem
2018
Discrete and Continuous Dynamical Systems. Series S
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We consider the Cauchy problem where Γ 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 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. 2010 Mathematics Subject Classification.
doi:10.3934/dcdss.2018051
fatcat:v7v7yyhygbb7tjged5myoys2s4