On the Operator Splitting Method: Nonlinear Balance Laws and a Generalization of Trotter-Kato Formulas

Abstract

Two different applications of the operator splitting method are presented here. The first one concerns hyperbolic systems of balance laws in one space dimension: we state the existence and the stability of solutions for initial data with bounded variation. As an example a case of vehicular traffic flow is then considered. The second application concerns abstract nonlinear semigroups in a metric space: we show how a composition of semigroups can be defined, thus generalizing Trotter-Kato product formulas to nonlinear semigroups.