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Global weak solutions to degenerate coupled diffusion-convection-dispersion processes and heat transport in porous media

In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in all transport coefficients are overcome by proving suitable a-priori $L^{\infty}$-estimates for the approximations of primary unknowns of the system.