Abstract
The time dependent neutron transport equation in a nonhomogeneous slab with generalized boundary conditions in the setting of L 1is studied. For the transport operator Aand the C0semigroup T(t) generated by A, it is shown under fairly general assumptions that the accumulation points of Pas(A) : σ(A) ∩ {λ : Reλ > −λ*}, if they exist, can only appear on the line Reλ = −λ*, where λ*is the essential infimum of the total collision frequency. Further, the spectrum of T(t) outside the disk {λ : |λ| ≤ exp(−λ* t)} consists of isolated eigenvalues of T(t) with finite algebraic multiplicity, and the accumulation points of σ(T(t)) ∩ {λ : |λ| > exp(−λ* t)}, if they exist, can only appear on the circle {λ : |λ| = exp(−λ* t)}.
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