Relaxation Limit and Initial-Layer for a Class of Hyperbolic-Parabolic Systems

Vincent Giovangigli (1) , Zaibao Yang (2) , Wen-An Yong (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 ZCAM - Zhou Pei-Yuan Center for Applied Mathematics

We consider a class of hyperbolic-parabolic systems with small diffusion terms and stiff sources. Existence of solutions to the Cauchy problem with ill prepared initial data is established by using composite expansions including initial-layer correctors and a convergence-stability lemma. New multitime expansions are introduced and lead to second-order error estimates between the composite expansions and the solution. Reduced equilibrium systems of second-order accuracy are also investigated as well as initial-layers of Chapman-Enskog expansions.

Mots clés: hyperbolic- parabolic system; stiff source; relaxation; initial-layer; ill prepared initial data

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Vincent Giovangigli, Zaibao Yang, Wen-An Yong. Relaxation Limit and Initial-Layer for a Class of Hyperbolic-Parabolic Systems. 2018. ⟨hal-01710330⟩