\(L^\infty \) Stationary Solutions to Non Homogeneous Conservation Laws

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 \({\textbf{L}^\infty }\) , no bound on the total variation is to be expected, and all discontinuities are entropy admissible.