| Abstrakt: |
We consider the Cauchy problem for a one-dimensional p-system with damping of space-dependent coefficient. This system models the compressible flow through porous media in the Lagrangian coordinate. Our concern is an asymptotic behavior of solutions, which is expected to be the diffusion wave based on the Darcy law. In fact, in the constant coefficient case Hsiao and Liu [Comm. Math. Phys., 143 (1992), pp. 599-605] showed the asymptotic behavior under suitable smallness conditions for the first time. After this work, there has been much literature, but there are few works that focus on the space-dependent damping case, as far as we know. In this paper we treat this space-dependent case, as a first step when the coefficient is around some positive constant. [ABSTRACT FROM AUTHOR] |
