Self-generation and nonlinear diffusion – an analytic approach

Abstract

The problem of simultaneous diffusion and creation processes, in particular self-generating mechanisms, is analysed with special regard to localization, dynamic confluence, collapse and anti-collapse. Exact solutions and central expansions for one- and multidimensional systems are developed. The analysis comprises a study of the case, where the coefficient of the self-generation source term is spatially inhomogeneous.