The nonlinear diffusion equation: asymptotic solutions and statistical problems

Front Matter....Pages I-X
Introduction....Pages 1-8
The Hopf-Cole Solution of the Nonlinear Diffusion Equation and Its Geometrical Interpretation for the Case of Small Diffusivity....Pages 9-20
Digression on Generalizations of the Geometric Method of Solution. — Solutions of Equation (1.1) for the Domain x > 0 with a Boundary Condition at x = 0....Pages 21-34
Statistical Problems Connected with the Solutions of Chapter I, for v →+0 and t →∞....Pages 35-45
Solutions of the Linear Diffusion Equation with a Boundary Condition Referring to a Parabola....Pages 46-71
Development of the Functions Ψ, E, F in Terms of Exponentials Multiplied By Bessel Functions....Pages 72-83
Evaluation of Integrals and Sums Depending on the Functions ѱ, E, F ....Pages 84-123
Mean Values Connected with the Sawtooth Curve of Figure 5....Pages 124-131
Distribution Functions Referring to Sets of Two Consecutive Arcs....Pages 132-151
Correlation Functions and Distribution Functions Referring to Sets of More Than Two Consecutive Arcs....Pages 152-173
Back Matter....Pages 174-174