Premium
L 1 asymptotic behavior of compressible, isentropic, viscous 1‐D flow
Author(s) -
Zeng Yanni
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470804
Subject(s) - pointwise , isentropic process , mathematics , compressibility , compressible flow , space (punctuation) , flow (mathematics) , mathematical analysis , mathematical physics , diffusion , mechanics , physics , thermodynamics , geometry , linguistics , philosophy
We study the large time behavior in L 1 of the compressible, isentropic, viscous 1‐D flow. Under the assumption that the initial data are smooth and small, we show that the solutions are approximated by the solutions of a parabolic system, and in turn by diffusion waves, which are solutions of Burgers equations. Decay rates in L 1 are obtained. Our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system. © 1994 John Wiley & Sons, Inc.