We consider the Cauchy problem for linear and quasilinear symmetrizable hyperbolic systems with coefficients depending on time and space, not smooth in $t$ and growing at infinity with respect to $x.$ We discuss well posedness in weighted Sobolev spaces, showing that the non-Lipschitz regularity in $t$ has an influence not only on the loss of derivatives of the solution but also on its behaviour for $|x| \rightarrow \infty.$ We provide examples to prove that the latter phenomenon cannot be avoided.

Log-Lipschitz regularity for SG-hyperbolic systems

ASCANELLI, Alessia;CAPPIELLO, Marco
2006

Abstract

We consider the Cauchy problem for linear and quasilinear symmetrizable hyperbolic systems with coefficients depending on time and space, not smooth in $t$ and growing at infinity with respect to $x.$ We discuss well posedness in weighted Sobolev spaces, showing that the non-Lipschitz regularity in $t$ has an influence not only on the loss of derivatives of the solution but also on its behaviour for $|x| \rightarrow \infty.$ We provide examples to prove that the latter phenomenon cannot be avoided.
2006
Ascanelli, Alessia; Cappiello, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1199477
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