L ∞ Stationary Solutions to Non Homogeneous Conservation Laws

Rinaldo M. Colombo (1) , Vincent Perrollaz (2) , Abraham Sylla (3)

1 UniBs - Università degli Studi di Brescia = University of Brescia
2 IDP - Institut Denis Poisson
3 UNIMIB - Università degli Studi di Milano-Bicocca = University of Milano-Bicocca

Stationary solutions, besides being relevant on their own, play a key role in a variety of analytic techniques related to conservation laws. Here, we present the construction of a (partial) foliation of stationary solutions to scalar conservation laws with x dependent fluxes. Differently from what happens in the x independent case, here solutions are in only bounded, no bound on the total variation is to be expected, and all discontinuities are entropy admissible.

Mots clés: Inverse design for hyperbolic equations; Conservation laws; Hamilton-Jacobi equation

Domaines: Equations aux dérivées partielles [math.AP]

Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla. L ∞ Stationary Solutions to Non Homogeneous Conservation Laws. 2023. ⟨hal-04046228⟩