- The theory of spiral structure of rotationally supported disk-shaped galaxies has a long history, but is not yet complete. Even though no definitive answer can be given at the present time, the majority of experts in the field is yielded to opinion that the study of the stability of gravity perturbations (e.g., those produced by spontaneous disturbances) in disk galaxies of stars is the first step towards an understanding of the phenomenon. We analyse the reaction between almost aperiodically growing Jeans-unstable gravity perturbations and stars of a rotating and spatially inhomogeneous disk of highly flattened galaxies. A mathematical formalism in the approxi-mation of weak turbulence (a quasi-linearization of the Boltzmann collisionless kinetic equation) is developed, which is a direct analogy with the plasma quasi-linear (weakly nonlinear) formalism. A diffusion equation in configuration space is derived which describes the change in the main body of equilibrium distribution of stars. The distortion in phase space resulting from such a wave-star interaction is studied. The theory, applied to the Solar neighborhood, accounts for the increase in the random stellar velocities with age and the essential radial spread of the Galaxy's disk. We argue that the Sun has migrated from its birth-place at the galactocentric radius r = 6 − 7 kpc in the inner part of the Galaxy outwards by ∆R ⊙ = 2 − 3 kpc during its lifetime of t ≈ 4.5 × 10 9 yr. This ∆R ⊙ is in fair agreement with the estimate of Wielen et al. (1996) ∆R ⊙ ≈ 1.9 kpc based on a radial galactic gradient in metallicity.