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;
2007-01-01
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.
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