Existence d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels. (French) Zbl 0692.35063

For symmetrizable quasilinear hyperbolic systems \[ \partial v/\partial t+A_ 1(v)\partial v/\partial x+\sum^{n}_{i=1}A_ 2^{(i)}\partial v/\partial y_ i=0, \] hypersurface \(x=\phi_ 0(y)\) \((\phi_ 0\) real, \(\phi_ 0\in C^{\infty}\), \(\phi_ 0(0)=\phi '_ 0(0)=0)\) there are given the data: \(v(x,y,0)=v_+(x,y)\) if \(x>\phi_ 0(y)\) and \(v(x,y,0)=v_-(x,y)\) if \(x<\phi_ 0(y)\). Local existence of rarefaction wave solutions is proved corresponding to a simple real genuinely nonlinear eigenvalue of the system.
Reviewer: L.G.Vulkov


35L60 First-order nonlinear hyperbolic equations
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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