Downloads & Free Reading Options - Results

This final report briefly summarizes the development and application of approximation and bounding techniques to nonlinear diffusion equations modelling phenomena in lubrication theory, combustion theory, heat flow, etc. The development of mathematical techniques has been guided by the need to meet physical problems. The mathematical techniques have been used to illuminate the behavior of models of various nonlinear diffusion phenomena. Techniques include monotone approximation schemes and nonlinear comparison theorems. These permit, for example, deriving bounds on solutions of nonlinear diffusion equations by finding functions which satisfy appropriate sets of differential inequalities. A typical application of these techniques has been the exploration of the relation between the stationary approximation of combustion theory and the full, time-dependent model. (Author)