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Integrability of a class of systems of conservation laws. (Intégrabilité d’une classe de systèmes de lois de conservation.) (French) Zbl 0769.35040

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.

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

Citations:

Zbl 0559.35046
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