On an Exactly Solvable Nonlinear Diffusion Equation
A nonlinear integro-differential equation describing a diffusion process with non-local mutual interaction is considered. It can be exactly linearized by a dependent variable transformation. A perturbational approach is employed to understand the structure of solutions of the equation. First, a series of differential equations approximating the integro-differential equation is derived. Then the effect of higher order corrections on the equilibrium solution is investigated.
KeywordsExact Solution Equilibrium Solution High Order Correction Variable Transformation Perturbational Approach
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- 5.J.Satsuma and M.Mimura: preprint, “Exact Treatment of Nonlinear Diffusion Equations with Singular Integral Terms”Google Scholar