Asymptotic Analysis of Nonlinear Diffusion and Related Multidimensional Integrals

In many important physical systems involving both diffusion and nonlinearity it often occurs that initially diffusion is the dominant mechanism. The question then arises as to whether or not linearization provides a uniformly valid first approximation for large times. The author attempts to partially answer this question by examining a number of simple model equations, both deterministic and stochastic. Several of the models are physically important and have been treated incorrectly in recent works. A major part of the analysis involves constructing asymptotic expansions for an interesting class of multidimensional integrals. (Author)