Generalized Solutions Of A Kind Of Quasilinear Degenerate Parabolic Equations Of Second Order

Nonlinear diffusion equations, as an important class of parabolic equations, come from a variety of diffusion phenomena appeared widely in nature. They are suggested as mathematical models of physical problems in many fields such as filtration, phase transition, biochemistry and dynamics of biological groups . Comparing to linear equations and quasilinear equations without degeneracy and singularity, such equations, to a certain extent, reflect even more exactly the physical reality.In this paper, we investigate the generalized solutions of a kind ofquasilinear degenerate parabolic equations of second order. InChapter1,we give the definition of the generalized solutions. In Chapter 2, wediscuss the existence and the uniqueness of the generalized solutions inone dimensional case. In Chapter 3, we study a special highdimensional case. In Chapter 4, we consider the regularity of the generalized solutions.