We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. Its solution describes the density evolution of interacting particles whose mobility is hampered by their aggregation. When the initial data lies below a Maxwellian, we derive the global wellposedness with instantaneous smoothness. The proof relies on hypoelliptic analogue of the classical parabolic theory, as well as a positivity-spreading result based on the Harnack inequality and barrier function methods. Moreover, the scaled equation leads to the fast diffusion flow under the low field limit. The relative phi-entropy method enables us to see the connection between the overdamped dynamics of the nonlinearly coupled kinetic model and the correlated fast diffusion. The global in time quantitative diffusion asymptotics is then derived by combining entropic hypocoercivity, relative phi-entropy and barrier function methods. Contents1. Introduction 1 2. Preliminaries 6 3. Kolmogorov-Fokker-Planck equation 8 4. Well-posedness of the nonlinear model 11 5. Diffusion asymptotics 22 Appendix A. Maximum principle 30 Appendix B. Spreading of positivity 31 Appendix C. Gaining regularity of spatial increment 33 References 34

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This article aims to the local boundedness and Hölder continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and transport. Although the equation is parabolic only in the velocity variable, it has a hypoelliptic structure provided that the transport part ∂t + b(v) • ∇x is nondegenerate in some sense. We achieve the results by revisiting the method, proposed by F. Golse, C. Imbert, C. Mouhot and A. Vasseur in the case b(v) = v, that combines the elliptic De Giorgi-Nash-Moser theory with velocity averaging lemmas.

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An innovative method is proposed to prepare artificial columnar jointed rock masses (CJRM) with different columnar dip angles, and laboratory physical model tests are conducted to investigate anisotropic permeability and porosity characteristics of the prepared artificial CJRM. In the physical model experiment, permeability and porosity of artificial CJRM with different columnar dip angles is measured during three times cyclic loading and unloading of confinement pressure. Based on the results of the laboratory model tests, the Equivalent Continuum Media Model was applied to analyse anisotropic permeability of CJRM. The main conclusions are summarized as follows. In the first loading phase of confinement pressure, the impacts of confinement pressure on the anisotropic permeability of artificial CJRM, porosity, and the major and minor principle permeability coefficients (PPCs) are significant, while in the following stages of confinement pressure loading and unloading, the change of them is small, with stable value. Permeability of artificial CJRM gradually increases with rise of columnar dip angle, and the permeability anisotropy of artificial CJRM under low confinement pressure is higher than that under low confinement pressure.