描述膜系统亚扩散的分数阶双曲型与抛物型方程
Hyperbolic versus parabolic equation with fractional derivative to describe subdiffusion in a membrane system
摘要：
我们用具有分数阶时间导数的抛物型和双曲型方程来描述薄膜系统中的次扩散。我们发现格林函数和解决方案的方程的系统中，均匀的解决方案是由一个薄膜分离的纯溶剂。在两个边界条件下获得的解决方案，其中膜表面的浓度的比率不随时间变化，并且其中流过膜的通量与膜表面之间的浓度差成比例。讨论了抛物型和双曲型次扩散方程在两种边界条件下的解之间的差异。
英文摘要：
We use the parabolic and hyperbolic equation with fractional time derivative to describe the subdiffusion in a system with thin membrane. We find the Green's function and solutions of the equation for the system where the homogeneous solution is separated by a thin membrane from the pure solvent. The solutions were obtained for two boundary conditions where the ratio of the concentrations at the membrane surfaces does not change in time and where the flux flowing through the membrane is proportional to the concentration difference between membrane surfaces. We discuss the difference between the solutions for parabolic and hyperbolic subdiffusion equations obtained for both boundary conditions.
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