Initial boundary value problem for the system of compressible adiabatic flow through porous media
The authors study the initial value problem for the system of compressible adiabatic flow through porous media in one space dimension with fixed boundary conditions. The global existence and uniqueness for the classical solution are obtained and the exponential convergence to a stationary state is established. Estimates of the solution are derived under restrictions concerning the oscillations in the initial data. It is also shown that the problem can be approximated very well time-asymptotically by an initial boundary problem for the related diffusion equations obtained from the original hyperbolic system by Darcy's law, provided that the initial total mass is the same. The difference between these two solutions tends to zero exponentially fast as time goes to infinity. The diffusive phenomena caused by damping mechanism with boundary effects are thus observed.
scientific article; zbMATH DE number 1389124