Ambrosio, L; Crippa, G; Figalli, A; Spinolo, L V (2011). Existence and uniqueness results for the continuity equation and applications to the chromatography system. In: Bressan, A; Chen, G Q G; Lewicka, M; Wang, D. Nonlinear conservation laws and applications. Proceedings of the summer program, IMA, Minneapolis, MN, USA, July 13-31, 2009. New York, NY, US: Springer, 195-204.
Abstract
We discuss some new well-posedness results for the continuity equation in arbitrary space dimension and we then illustrate applications to a system of conservation laws in one space dimension known as the chromatography system. In the last section, we discuss some related open problems.