Well Posedness and Characterization of Solutions to Non Conservative Products in Non Homogeneous Fluid Dynamics Equations

Abstract Consider a balance law where the flux depends explicitly on space variable. At jump discontinuities, modeling considerations may impose defect in conservation of some quantities, thus leading to non conservative products. Below, we deduce evolution smooth case from conditions at discontinuities. Moreover, resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, flow water canal with varying width depth, as inviscid Euler equations pipes geometry.