Weak solutions of coupled dual porosity flows in fractured rock mass and structured porous media

This paper deals with a fully nonlinear degenerate parabolic system with natural (critical) growths and under non-linear boundary conditions. Such problems arise from the heat and water flow through a partially saturated fractured rock mass and structured porous media. Existence of a global weak solution of the problem (on an arbitrary interval of time) is proved by means of semidiscretization in time, deriving suitable a-priori estimates based on W1,pW1,p-regularity of the approximate solution and by passing to the limit from discrete approximations.