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

被引:39
作者
Plastino, AR
Casas, M [1 ]
Plastino, A
机构
[1] Univ Illes Balears, Dept Fis, E-07071 Palma de Mallorca, Spain
[2] Natl Univ La Plata, Fac Astron & Geophys, RA-1990 La Plata, Argentina
[3] Argentine Natl Res Council, CONICET, RA-1900 La Plata, Argentina
[4] Natl Univ La Plata, Dept Fis, RA-1900 La Plata, Argentina
关键词
nonlinear diffusion; Tsallis thermostatistics; reaction-diffusion equations; population dynamics;
D O I
10.1016/S0378-4371(00)00006-6
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:289 / 303
页数:15
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