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Study of a transport operator with unbounded coefficients

Abstract : In this paper we study the transport operator given by the sum of a free-streaming term and of an absorption term. The velocity coefficient appearing in the definition of the operator is unbounded ($v\in {\RR}$) while the position coordinate belongs to the one-dimensional bounded set $[-b, +b]$. The boundary condition associated to the transport operator are given by means of a bounded and positive operator $\Lambda$. We prove that an evolution problem associated to the above transport operator has a unique positive solution whose explicit form is given by means of a $C_0$-semigroup in the case $\Vert \Lambda \Vert \leq 1$ and by means of an integrated semigroup or a $C$-semigroup in the case $\Vert \Lambda \Vert >1$.
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Submitted on : Wednesday, October 24, 2012 - 11:07:54 PM
Last modification on : Monday, March 16, 2020 - 8:02:08 PM
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  • HAL Id : hal-00076880, version 1



Simona Mancini, Silvia Totaro. Study of a transport operator with unbounded coefficients. Advances in Mathematical Sciences and Applications, GAKKO TOSHO TOKYO, 2002, 12, 1, pp.377-391. ⟨hal-00076880⟩



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