Abstract
We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (t, x) ∈ [0, T ] × ℝn and presenting a linear growth for |x | ∞. We prove well-posedness in the Schwartz space (ℝn). The result is obtained by deriving an energy estimate for the solution of the linearized problem in some weighted Sobolev spaces and applying a fixed point argument. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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