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Fractional nonlinear diffusion equation, solutions and anomalous diffusion

Author

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  • Silva, A.T.
  • Lenzi, E.K.
  • Evangelista, L.R.
  • Lenzi, M.K.
  • da Silva, L.R.

Abstract

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.

Suggested Citation

  • Silva, A.T. & Lenzi, E.K. & Evangelista, L.R. & Lenzi, M.K. & da Silva, L.R., 2007. "Fractional nonlinear diffusion equation, solutions and anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 65-71.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:1:p:65-71
    DOI: 10.1016/j.physa.2006.09.001
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    Citations

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    Cited by:

    1. Estrada, Ernesto & Sheerin, Matthew, 2017. "Random neighborhood graphs as models of fracture networks on rocks: Structural and dynamical analysis," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 360-379.
    2. Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.
    3. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
    4. 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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