First order quasilinear equations with boundary conditions in the $L^\infty$ framework

Sébastien Martin (1)

1 ICJ - Institut Camille Jordan

We study a class of first order quasilinear equations on bounded domains with $L^\infty$ data. Using the "semi Kruzkov entropy-flux pairs", we define a weak-entropy solution, state an existence and uniqueness result, and a set preserving result.

Mots clés: Doubling variable method

Mots clés: Semi Kruzkov entropy-flux pair; Set preserving property; BV estimates; Vanishing viscosity method; Doubling variable method.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Sébastien Martin. First order quasilinear equations with boundary conditions in the $L^\infty$ framework. 2007. ⟨hal-00007856v2⟩