Monotone iterative technique for partial differential equations of first order (Q1059211)

The authors are concerned with a monotone iterative technique for first- order partial differential equations of the form \(u_ t+\sum^{n}_{i=1}f_ i(t,x)u_{x_ i}=g(t,x,u),\) for \(0\leq t\leq T\) and \(a\leq x=(x_ 1,...,x_ n)\leq b\) \((a,b\in {\mathbb{R}}^ n)\). To this purpose they prove existence, uniqueness and comparison results. At last, an application to the construction of Lyapunov functions is given.