Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:C2L-B
Session:
Number:C2L-B1
Geometric aspects of a certain type of nonlinear diffusion equations
Atsumi Ohara, Tatsuaki Wada,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized exponential densities. Next by equipping the so-called q-Gaussian densities with such structure, we show several physically and geometrically interesting properties of the solutions, e.g., characterization of the moment-conserving projection of a solution, evaluations of evolutional velocities of the second moments and the convergence rate to the manifold in terms of the geodesic curves, divergence and so on.