Abstract: In this paper the abstract boundary value problem on Hilbert space H is studied:
T d/dx=-A(x)ψ(x)+f(x) 0 < x < a Q+ψ(0)=a₁Q+ψ(a)+g₊ 0<a₁,a₂ ≤ 1 Q-ψ(a)=a+2Q-ψ(0)+g_-
where Q₊/Q_- are the maximum positive/negative spectral projections of self-adjoint operator T. Under suitable conditions, it is shown that the boundary value problem of abstract kinetic equation is well-posed and can be applied to transport theory.