$L^1$ Nonlinear Stability of Travelling Waves for Hyperbolic System with Relaxation

Corrado Mascia (1) , Natalini Roberto (2)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

The Jin-Xin 2×2 semilinear hyperbolic system is considered. Under a natural assumption, the subcharacteristic condition (suitably localised to the context of travelling waves), it is shown that solutions arising from perturbations of travelling wave initial data converge time asymptotically in L^1 to translates of the unperturbed travelling wave solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Corrado Mascia, Natalini Roberto. $L^1$ Nonlinear Stability of Travelling Waves for Hyperbolic System with Relaxation. Journal of Differential Equations, 1996, 132 (2), pp.275-292. ⟨hal-00881859⟩