A reaction infiltration problem: classical solutions
John Chadam, Xinfu Chen, Roberto Gianni, Riccardo Ricci · Proceedings of the Edinburgh Mathematical Society · 1997
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. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.