We consider "forward-backward" parabolic equations in the abstract form Jdψ/dx+Lψ=0, 0<x<τ≤∞, where J and L are
operators in a Hilbert space H such that J=J∗=J−1, L=L∗≥0, and
kerL=0. The following theorem is proved: if the operator B=JL is
similar to a self-adjoint operator, then associated half-range boundary
problems have unique solutions. We apply this theorem to corresponding
nonhomogeneous equations, to the time-independent Fokker-Plank equation μ∂x∂ψ(x,μ)=b(μ)∂μ2∂2ψ(x,μ), 0<x<τ, μ∈R, as well as to
other parabolic equations of the "forward-backward" type. The abstract kinetic
equation Tdψ/dx=−Aψ(x)+f(x), where T=T∗ is injective and
A satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in
the introductio