A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations

A.R. Plastino, M. Casas and A. Plastino

Physica A: Statistical Mechanics and its Applications, 2000, vol. 280, issue 3, 289-303

Abstract: We consider a monoparametric family of reaction–diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time-dependent particular solutions of the Tsallis’ maximum entropy (MaxEnt) form. The evolution of these solutions is governed by a system of three coupled nonlinear ordinary differential equations that are integrated numerically. A simple population dynamics interpretation provides a qualitative understanding of the behaviour of the q-MaxEnt solutions. When the reaction term vanishes the time-dependent distributions studied here reduce to the previously known Tsallis’ MaxEnt solutions for the nonlinear diffusion equation.

Keywords: Nonlinear diffusion; Tsallis thermostatistics; Reaction–diffusion equations; Population dynamics (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:280:y:2000:i:3:p:289-303

DOI: 10.1016/S0378-4371(00)00006-6

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