Existence of solution of a forest fire spread model

Abstract

We consider a wildfire spread model represented by the system (1) . We use results from the theory of Hamilton–Jacobi equations to prove that there exists a classical solution of (1) for any ( ϕ , t ) ∈ R × ( 0 , T ) and some T > 0 and satisfies particular initial conditions. We also use the method of characteristics to obtain the solution of (1) in a certain form.