  This paper is concerned with the development and analysis of a mathematical
model that is motivated by interstitial hydrodynamics and tissue deformation
mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumor. The
classical mixture theory is adopted for mass and momentum balance equations for
a two-phase system. A main contribution of this study, we treat the
physiological transport parameter (i.e., hydraulic resistivity) as anisotropic
and heterogeneous, thus the governing system is strongly coupled and nonlinear.
We derived a weak formulation and then formulated the equivalent fixed-point
problem. This enabled us to use the Galerkin method, and the classical results
on monotone operators combined with the well-known Schauder and Banach fixed
point theorems to prove the existence and uniqueness results.
