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

Author

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  • Plastino, A.R.
  • Casas, M.
  • Plastino, A.

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.

Suggested Citation

  • Plastino, A.R. & Casas, M. & Plastino, A., 2000. "A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 289-303.
    • Handle: RePEc:eee:phsmap:v:280:y:2000:i:3:p:289-303
    DOI: 10.1016/S0378-4371(00)00006-6
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    Cited by:

    1. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Lenzi, E.K. & Ribeiro, M.A. & Fuziki, M.E.K. & Lenzi, M.K. & Ribeiro, H.V., 2018. "Nonlinear diffusion equation with reaction terms: Analytical and numerical results," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 254-265.

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