| Abstract: |
| We present some results on the blow-up of systems of semilinear coupled waves with scale-invariant damping and time-derivative nonlinearities, examining various scenarios that include mass terms and time-dependent propagation speeds. A key novelty lies in a more refined characterization of the blow-up region, with a particular focus on the impact of the Tricomi term, which significantly alters the dynamics of the system. These findings relate to the well-known Glassey exponent. From a numerical perspective (Lattice Boltzmann methods and PINNs), we explore a tentative of blow-up time detection for some toy models. The determination of the threshold between blow-up and global existence regions is an interesting problem, but here we intend to provide some numerical insights for proving the conjectures on the critical nonlinearity exponent. |
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