We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (t, x) \in [0, T ] \times R^n and presenting a linear growth for |x | tending to + infinity. We prove well-posedness in the Schwartz space S(R^n). 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.

THE CAUCHY PROBLEM FOR QUASILINEAR SG-HYPERBOLIC SYSTEMS

CAPPIELLO, Marco;ZANGHIRATI, Luisa
2007

Abstract

We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (t, x) \in [0, T ] \times R^n and presenting a linear growth for |x | tending to + infinity. We prove well-posedness in the Schwartz space S(R^n). 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
Cappiello, Marco; Zanghirati, Luisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/495732
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