A Regularizing Eeect of Nonlinear Transport Equations
نویسنده
چکیده
We consider the semigroup on L 1 (IR n) deened by the nonlinear transport equation for the scalar s @ t s + div(f(s) u) = 0 in (0; 1)I R n for given velocity eld u. We show that this nonlinear semigroup is HH older continuous for t > 0 in the uniform operator topology, provided the graph of f has no linear segments. This continuity property | which expresses a regularizing eeect of the nonlinearity in the transport equation | is robust with respect to the spatial behaviour of the time{independent velocity eld u.
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تاریخ انتشار 1998