Generalized multiplying boundary conditions in a rod and B-bounded semigroups

Abstract : A transport problem for the particle density function $n(x,v,t)$ in the bounded region $[-b,+b]$ is considered. The particle velocities are assumed to be unbounded. The boundary conditions are expressed by means of a general {\em multiplying} boundary operator $\Lambda$, relating the incoming and outgoing flux of particles. The generation of a B-bounded semigroup (see [1], [2], [3]) is proved, and the solution of the transport problem is explicitly given by means of the B-bounded semigroup.
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Simona Mancini. Generalized multiplying boundary conditions in a rod and B-bounded semigroups. CEMRACS 99, 2001, France. pp.141-149. ⟨hal-00076879⟩

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