We start with (Single-phase pressure diffusion @model:1):
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and neglect the non-linear term c \cdot ( {\bf u} \, \nabla p) for low compressibility fluid c \sim 0.
Together with constant pore compressibility c_r = \rm const this will lead to constant total compressibility c_t = c_r + c \approx \rm const.
Assuming that permeability and fluid viscosity do not depend on pressure k(p) = k = \rm const and \mu(p) = \mu = \rm const one arrives to the differential equation with constant coefficients:
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See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model / Single-phase pressure diffusion @model