Pre-Publicación 2026-19
Fahim Aslam, Marcelo Cavalcanti, Zayd Hajjej, You Haiyang Lin Bo, Mauricio Sepúlveda:
Blow-up of a Lamé system with fractional damping and infinite memory: theoretical and numerical study
Abstract:
This paper investigates finite-time blow-up phenomena for a Lamé-type system with memory effects. Under suitable assumptions on the relaxation functions and for initial data with sufficiently low energy, we establish a finite-time blow-up result for the corresponding solutions. In addition to the theoretical analysis, we develop a numerical approximation based on a finite volume method combined with a Newmark-type time discretization. The numerical experiments illustrate the qualitative behavior predicted by the theory, reproduce the decay dynamics in the stable regime, and capture the onset of blow-up, thereby confirming the effectiveness and reliability of the proposed numerical scheme.
