We show that the framework of quasidifferential equations in metric spaces can be effectively used to obtain different well posedness results for nonlinear systems of balance laws. In particular, we will present a recent result which improves the theory of quasidifferential equations in metric spaces as introduced in \cite{BressanLarnas,Panasyuk,Panasyuk97}. Having the classical theory of ordinary differential equations as driving example, this theory comprises various other situations, from Hille-Yosida Theorem to operator splitting in metric spaces. The following cases will be considered: balance laws with (possibly) non local sources and balance laws with boundary which comprises balance laws at a junction.
Guerra, G., Colombo, R. (2009). Balance laws as quasidifferential equations in metric spaces. In A.E. Tzavaras, E. Tadmor, J.G. Liu (a cura di), Hyperbolic problems: theory, numerics, applications (pp. 527-536). Providence : American Mathematical Society.
Balance laws as quasidifferential equations in metric spaces
GUERRA, GRAZIANO;
2009
Abstract
We show that the framework of quasidifferential equations in metric spaces can be effectively used to obtain different well posedness results for nonlinear systems of balance laws. In particular, we will present a recent result which improves the theory of quasidifferential equations in metric spaces as introduced in \cite{BressanLarnas,Panasyuk,Panasyuk97}. Having the classical theory of ordinary differential equations as driving example, this theory comprises various other situations, from Hille-Yosida Theorem to operator splitting in metric spaces. The following cases will be considered: balance laws with (possibly) non local sources and balance laws with boundary which comprises balance laws at a junction.
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