Applications bilinéaires compatibles avec un système hyperbolique. (Bilinear maps compatible with a hyperbolic system). (French) Zbl 0601.35066

Hanouzet, Bernard; Joly, Jean-Luc

C. R. Acad. Sci., Paris, Sér. I 301, 491-494 (1985).

To each pair (u,v) of solutions of \({\mathcal L}u=0\) where \({\mathcal L}\) is an \(N\times N\) hyperbolic system we can associate the function q(u,v)(t,x), \(t\in {\mathbb{R}}\), \(x\in {\mathbb{R}}^ n\), with q a given bilinear form on \({\mathbb{C}}^ N\times {\mathbb{C}}^ N\). The asymptotic behaviour of q(u,v)(t,.) when [t] grows to infinity allows us to introduce several families of bilinear form (we call them compatible with \({\mathcal L})\) which define a weaker coupling.

MSC:

35L40	First-order hyperbolic systems
35B40	Asymptotic behavior of solutions to PDEs
35E20	General theory of PDEs and systems of PDEs with constant coefficients

Keywords:

hyperbolic system; asymptotic behaviour