Serre, Denis Integrability of a class of systems of conservation laws. (Intégrabilité d’une classe de systèmes de lois de conservation.) (French) Zbl 0769.35040 Forum Math. 4, No. 6, 607-623 (1992). Explicit integration formulae for the Cauchy problem to hyperbolic systems of \(n\) equations \(\partial _ tu+\partial _ xf(u)=0\) having \(p\) families of invariant linear submanifolds [see B.Temple: Systems of conservation laws with invariant submanifolds, Trans. Am. Math. Soc. 280, 781-795 (1983; Zbl 0559.35046)] are given. These formulae reduce for \(n=1\) to the well known calculus for Hamilton-Jacobi equations. The author also proves the existence of almost-periodic solutions of the above system with periodic and Lipschitz initial data. The applications concern chromatography, electrophoresis and special linearly degenerate systems. Reviewer: M.Kopáčková (Praha) Cited in 5 Documents MSC: 35L65 Hyperbolic conservation laws 35L80 Degenerate hyperbolic equations 35L60 First-order nonlinear hyperbolic equations 35L45 Initial value problems for first-order hyperbolic systems 35B15 Almost and pseudo-almost periodic solutions to PDEs Keywords:Cauchy problem; families of invariant linear submanifolds; calculus for Hamilton-Jacobi equations; existence of almost-periodic solutions; periodic and Lipschitz initial data; linearly degenerate systems Citations:Zbl 0559.35046 PDFBibTeX XMLCite \textit{D. Serre}, Forum Math. 4, No. 6, 607--623 (1992; Zbl 0769.35040) Full Text: DOI EuDML