We investigated the scenario of time-dependent diffusive interaction between dark matter and dark energy and showed that such a model can be accommodated within the observations of luminosity distance-redshift data in Supernova Ia (SN Ia) observations. We obtain constraints on different relevant parameters of this model from the observational data. We consider a homogeneous scalar field ϕ(t) driven by a k-essence Lagrangian of the form L = V(ϕ)F(X) with constant potential V(ϕ) = V, to describe the dynamics of dark energy in this model. Using the temporal behaviour of the FRW scale factor, the equation of state and total energy density of the dark fluid, extracted from the analysis of SN Ia (JLA) data, we have obtained the time-dependence of the k-essence scalar field and also reconstructed the form of the function F(X) in the k-essence Lagrangian.

我们研究了暗物质和暗能量之间随时间变化的扩散相互作用的场景，并表明这种模型可以容纳在超新星 Ia (SN Ia) 观测中的光度距离-红移数据的观测中。我们从观测数据中获得了对该模型不同相关参数的约束。我们考虑一个均匀的标量场φ ( t ) 由形式为L = V ( φ ) F ( X ) 的k本质拉格朗日驱动，具有恒定电位V ( φ ) = V，来描述这个模型中暗能量的动态。使用从 SN Ia (JLA) 数据分析中提取的 FRW 比例因子的时间行为、状态方程和暗流体的总能量密度，我们获得了k本质标量场的时间依赖性和还重构了k本质拉格朗日函数F ( X ) 的形式。