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Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

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  • Wang, Jun
  • Zhang, Wen-Jun
  • Liang, Jin-Rong
  • Zhang, Pan
  • Ren, Fu-Yao

Abstract

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D(t,x)=D(t)|x|−θ, subject to absorbing boundary condition and the conventional initial condition p(x,0)=δ(x−x0). We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.

Suggested Citation

  • Wang, Jun & Zhang, Wen-Jun & Liang, Jin-Rong & Zhang, Pan & Ren, Fu-Yao, 2008. "Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4547-4552.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:18:p:4547-4552
    DOI: 10.1016/j.physa.2008.04.017
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    References listed on IDEAS

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    1. Wang, Jun & Zhang, Wen-Jun & Liang, Jin-Rong & Xiao, Jian-Bin & Ren, Fu-Yao, 2008. "Fractional nonlinear diffusion equation and first passage time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 764-772.
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