High-Order Nonlinear Diffusion

A number of important physical processes, such as the flow of a surface-tensiondominated thin liquid and the diffusion of dopant in semiconductors are governedby the fourth-order nonlinear diffusion equation u, + («"«*„),: = 0 (n > 0). Theanalysis of such equations is doubly complex due to the nonlinearity and the highorder. Here we present some of the more immediate and simple results for thisequation and our development parallels known results for the classical nonlineardiffusion equation u, = (u"u