A flame propagation model on a network with application to a blocking problem
A flame propagation model on a network with application to a blocking problem
We consider the Cauchy problem$\left\{ \begin{array}{*{35}{l}} {{\partial }_{t}}u+H(x,Du) = 0&(x,t)\in \Gamma \times (0,T) \\ u(x,0) = {{u}_{0}}(x)&x\in \Gamma \\\end{array} \right.$where $\Gamma$ 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 …