A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations |
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Authors: | A R Plastino M Casas A Plastino |
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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. |
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Keywords: | Nonlinear diffusion Tsallis thermostatistics Reaction– diffusion equations Population dynamics |
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