Quasi-static Limit for a Hyperbolic Conservation Law

Stefano Marchesani (1) , Stefano Olla (2) , Lu Xu (1)

1 GSSI - Gran Sasso Science Institute
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study the quasi-static limit for the $L^\infty$ entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with the quasi-static equation, whose entropy solution is determined by the stationary profile corresponding to the boundary data at a given time.

Mots clés: quasi-static limits; entropy solutions; boundary entropy flux; hyperbolic conservation laws

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Stefano Marchesani, Stefano Olla, Lu Xu. Quasi-static Limit for a Hyperbolic Conservation Law. Nonlinear Differential Equations and Applications, 2021, 28 (53), ⟨10.1007/s00030-021-00716-5⟩. ⟨hal-03177217v2⟩