Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping
Analysis of PDEs
2023-07-13 v1 Mathematical Physics
math.MP
Abstract
We consider the Cauchy problem for one-dimensional p-system with damping of space-dependent coefficient. This system models the compressible flow through porous media in the Lagrangean coordinate. Our concern is an asymptotic behavior of solutions, which is expected to be the diffusion wave based on the Darcy law. To show this expectation, the problem is reformulated to the Cauchy problem for the second order quasilinear hyperbolic equation with space dependent damping, which is analyzed by the energy method.
Keywords
Cite
@article{arxiv.2307.05865,
title = {Asymptotic behavior of solutions to the Cauchy problem for 1-D p-system with space dependent damping},
author = {Akitaka Matsumura and Kenji Nishihara},
journal= {arXiv preprint arXiv:2307.05865},
year = {2023}
}
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22 pages