Analysis of non-isothermal multiphase flows in porous media

We consider an initial-boundary value problem for a degenerate fully nonlinear parabolic system modeling coupled two-phase flow and heat transport through porous media. The two-phase fluid system consists of incompressible wetting phase and compressible nonwetting phase, such that the density of the nonwetting phase is a function of the phase pressure and temperature. To simplify the structure of the problem and overcome degeneracies in transport coefficients, the mathematical model is reformulated by using the feature of the so-called global pressure and the capillary pressure potential. Under physically relevant assumptions on the data of the problem and taking the initial conditions and mixed boundary conditions into consideration, we prove a global existence of a weak solution to this system on any physically relevant time interval.