2008/10/03 by Atsumi Ohara, Tatsuaki Wada, Ohara, Atsumi +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #advanced mathematical theories #cond-mat.stat-mech #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.0810.0624
minorly corrected; references added; to appear in Journal of Physics A: Mathematical and Theoretical
openalex publication_date 2008/10/03 · arxiv created 2009/12/16 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 considering such a structure in particular on the q-Gaussian densities, we derive several physically and geometrically interesting properties of the solutions. They include, for example, characterization of the moment-conserving projection of a solution, evaluation of evolutional velocities of the second moments and the convergence rate to the manifold in terms of the geodesic curves, divergence and so on.