  This paper is concerned with an uniqueness of solution of the weak
formulation of an evolution dam problem related to a compressible fluid flow
through a two-dimensional, rectangular and heterogeneous porous medium. Note
that our problem associated with the equation
a(x_1)(u_{x_2}+\chi)_{x_2}-(u+\chi)_t=0. Our technique is based on the idea
that we transform the weak form of this equation into a similar situation to
the proof of the uniqueness in the incompressible case (see [12]). It is also
difficult to adapt the proof obtained in [12] by using some properties of the
solutions as in [12, Sect. 2].

Analysis of PDEs