One-dimensional conservation law with boundary conditions: general results and spatially inhomogeneous case

Boris Andreianov (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

The note presents the results of the recent work \cite{AS-Tran} of K. Sbihi and the author on existence and uniqueness of entropy solutions for boundary-value problem for conservation law $u_t+\ph(u)_x=0$ (here, we focus on the simplified one-dimensional setting). Then, using nonlinear semigroup theory, we extend these well-posedness results to the case of spatially dependent flux $\ph(x,u)$.

Mots clés: General boundary condition; Entropy solution; Integral solution

Domaines: Equations aux dérivées partielles [math.AP]

Boris Andreianov. One-dimensional conservation law with boundary conditions: general results and spatially inhomogeneous case. 2012. ⟨hal-00761664v1⟩