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The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.

Uturuncu volcano (southwestern Bolivia) is localized within one of the largest updoming volcanic zones, the Altiplano Puna Volcanic Complex (APVC). In several geodetic studies the observed uplift phenomenon is analyzed and modeled by considering a deep source, related to the Altiplano Puna Magma Body (APMB). In this framework, we perform a multiscale analysis on the 2003–2010 ENVISAT satellite data to investigate the existence of a multi-source scenario for this region. The proposed analysis is based on Cross-correlation and Multiridge method, pointing out the spatial and temporal multiscale properties of the deformation field. In particular, we analyze the vertical component of ground deformation during two time interval: within the 2005–2008 time interval an inflating source at 18.7 km depth beneath the central zone of the APVC is retrieved; this result is in good agreement with those proposed by several authors for the APMB. Between August 2006 and February 2007, we identify a further inflating source at 4.5 km depth, beneath Uturuncu volcano; the existence of this latter, located just below the 2009–2010 seismic swarm, is supported by petrological, geochemical, and geophysical evidence, indicating as a possible interpretative scenario the action of shallow, temporarily trapped fluids.