Abstract: This paper has derived generalized Reynolds equation in lubrication theory in terms of tensor analysis and S-coordinate system, and has provided corresponding varia-tional inequality. The curved effect of flow of lubricant fluid is considered, and the influence of intrinsic properties of surfaces of axis and axle sleeve on flow are counted.

Key words: tumor growth, avascular, p27 gene, multi-scale, continuous-discrete model, numerical simulation, Airy functions, bianalytic functions, biharmonic functions, the uniqueness of the solution, integral representation formula