We present C_0-semigroup generation results for the free streaming operator with abstractboundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with many examples and show that our result applies to the physical cases of Maxwell boundary conditions in the kinetic theory of gases, as well as to the nonlocal boundary conditions involved in transport-like equations from population dynamics.
Semigroup generation properties of streaming operators with noncontractive boundary conditions.
LODS, BERTRAND
2005-01-01
Abstract
We present C_0-semigroup generation results for the free streaming operator with abstractboundary conditions. We recall some known results on the matter and establish a general theorem. We motivate our study with many examples and show that our result applies to the physical cases of Maxwell boundary conditions in the kinetic theory of gases, as well as to the nonlocal boundary conditions involved in transport-like equations from population dynamics.
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