Rossato R, Lenzi M K, Evangelista L R, Lenzi E K
Universidade Estadual de Maringá, Departamento de Física, Avenida Colombo 5790, 87020-900 Maringá, Paraná, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Sep;76(3 Pt 1):032102. doi: 10.1103/PhysRevE.76.032102. Epub 2007 Sep 10.
Surface effects on a diffusion process governed by a fractional diffusion equation in a confined region with spatial and time dependent boundary conditions are investigated. First, we consider the one-dimensional case with the boundary conditions rho(0,t)=Phi0(t) and rho(a,t)=Phia(t). Subsequently, the two-dimensional case in the cylindrical symmetry with rho(a,theta,t)=Phia(theta,t) and rho(b,theta,t)=Phib(theta,t) is investigated. For these cases, we also obtain exact solutions for an arbitrary initial condition by using the Green's function approach.
研究了在具有空间和时间相关边界条件的受限区域中，由分数扩散方程控制的扩散过程的表面效应。首先，我们考虑具有边界条件ρ(0,t)=Φ0(t)和ρ(a,t)=Φa(t)的一维情况。随后，研究了圆柱对称下的二维情况，其中ρ(a,θ,t)=Φa(θ,t)和ρ(b,θ,t)=Φb(θ,t)。对于这些情况，我们还通过使用格林函数方法获得了任意初始条件下的精确解。
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