A REACTION INFILTRATION PROBLEM: EXISTENCE, UNIQUENESS, AND REGULARITY OF SOLUTIONS IN TWO SPACE DIMENSIONS
John Chadam, Xinfu Chen, Roberto Gianni, Riccardo Ricci · Mathematical Models and Methods in Applied Sciences · 1995
In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. We establish global existence, uniqueness and regularity of the solution in a two-dimensional finite strip (−M, M)×(0, 1) and the existence and partial regularity of solutions in an infinite strip (−∞, ∞)×(0, 1).