标题： 多孔介质中退化耦合扩散-对流-色散过程和热传导的全局弱解 显示英文标题

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

摘要： 在本次贡献中，我们证明了由耦合的水分运动、溶解物质的迁移和部分饱和多孔材料中的热量传递所产生的退化抛物型方程组弱解的存在性。 考虑了物理上合理的混合狄利克雷-诺伊曼边界条件和初始条件。 通过时间的半离散化并从离散近似中取极限，证明了该问题全局弱解的存在性。 退化出现在非线性传输系数中，这些系数未被假定为由正常数上下界限定。 通过证明系统主要未知量近似值的适当先验$L^{\infty}$-估计，克服了所有传输系数中的退化。 显示英文摘要

摘要： 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.