Flow through a porous column
The general equations describing the steady-state flow through a porous column are assumed. In this paper, the existence, uniqueness and comparison results for the solutions of the equations with Dirichlet and mixed boundary conditions are obtained. The existence of a weak solution to the evolution problem is also deduced. The governing equations are highly nonlinear. Solutions are mostly in terms of inequalities. The method of finite differences and the idea of finite elements are used for the numerical solutions, even though such problems require more of analytical solution. Nevertheless, the paper is useful to scientists and engineers besides the mathematicians.
scientific article; zbMATH DE number 3959034