Abstract
We study the abstract differential equation\(T\frac{{\partial f}}{{\partial x}} + Af = 0\) on a Hilbert space H, which represents a variety of different kinetic equations. T is assumed bounded and self-adjoint on H, and A (unbounded) positive self-adjoint and Fredholm. For partial range boundary conditions and 0≤x<∞, we prove existence and (non-) uniqueness theorems and give representations of the solution. Various examples from neutron transport, radiative transfer of polarized and unpolarized light, and electron transport are given.
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This paper is dedicated to K.M. Case on the occasion of his sixtieth birthday
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Greenberg, W., van der Mee, C.V.M. & Zweifel, P.F. Generalized kinetic equations. Integr equ oper theory 7, 60–95 (1984). https://doi.org/10.1007/BF01204914
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DOI: https://doi.org/10.1007/BF01204914