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Linearization method to stability analysis for nonlinear hyperbolic systems. (English. Abridged French version) Zbl 1034.35069

Summary: It is shown that the linearization principle is true for a class of nonlinear hyperbolic systems with two independent variables, time and space. To keep clear exposition, our proof is based on the Saint Venant equation. More results can be proven by using the Lyapunov function candidate that we give here.

MSC:

35L60 First-order nonlinear hyperbolic equations
35L50 Initial-boundary value problems for first-order hyperbolic systems
35B35 Stability in context of PDEs
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