We investigate well posedness of the Cauchy problem for SG hyperbolic systems with non-smooth coefficients with respect to time. By assuming the coefficients to be Hoelder continuous we show that this low regularity has a considerable influence on the behaviour at infinity of the solution as well as on its regularity. This leads to well posedness in suitable Gelfand-Shilov classes of functions on R^n. A simple example shows the sharpness of our results.
Holder continuity in time for SG hyperbolic systems
CAPPIELLO, Marco
2008-01-01
Abstract
We investigate well posedness of the Cauchy problem for SG hyperbolic systems with non-smooth coefficients with respect to time. By assuming the coefficients to be Hoelder continuous we show that this low regularity has a considerable influence on the behaviour at infinity of the solution as well as on its regularity. This leads to well posedness in suitable Gelfand-Shilov classes of functions on R^n. A simple example shows the sharpness of our results.
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