Applied Mathematical Problems in Geophysics : Cetraro Italy 2019 This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management in particular the degradation of organic waste by an aerobic biomass by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1 dimensional boundary value problems in particular to light ray tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co seismic events associated to large earthquakes. This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.