With[{u = u[θ, ω]},
  eq = -D[ω u, θ] - D[-A Sin[θ] u, ω] - γ kT D[u, ω] + γ  D[ω u, ω]==0;

ufun = NDSolveValue[{eq, u[t, -π, ω] == u[t, π, ω], u[t, θ, ωcb] == u[t, θ, ωct]},
    u, {θ, -π, π}, {ω, ωcb, ωct}
    ];


   Plot3D[Abs[ufun[θ, ω]], {θ, -π, π}, {ω, ωb, ωt},
     PlotRange -> All, AxesLabel -> Automatic, PlotPoints -> 50,
    BoxRatios -> {Pi, ωb, 1}]