In this thesis we studied the potential that the next-generation neutrino detectors (JUNO, Hyper-Kamiokande and DUNE) will have to the detection of the Earth matter effects through the identification of the modulations in the energy spectrum of neutrinos from core-collapse supernovae in our galaxy, assuming the possibility of the invisible decay of v2 after the neutrinos have left the star, on their way to Earth. Recent simulations of gravitational collapse (and subsequent explosion) of stars more massive than ~ 8Mo show that during the cooling phase the average energies (EVe) and (Evx) become very similar and the fluxes tend to equalize, making it difficult to observe the Earth matter effects using a single detector. In this work we show that the inclusion of neutrino decay creates also the possibility of observing the effects under consideration in the neutrino detection channel if the mass ordering is normal and in the anti-neutrino channel if the ordering is inverted, which is not expected in the absence of neutrino decay. In particular, if the decay rate is more than ~ 70%, we find that the invisible neutrino decay of v2 can enhance the observation possibilities of Earth matter effects even for supernovae at a distance of 10 kpc from us.