Convergence rate from hyperbolic systems of balance laws to parabolic systems. Issue 5 (4th April 2021)

• Record Type: Journal Article
• Authors: Li, Yachun; Peng, Yue-Jun; Zhao, Liang
• Is Part Of: Applicable analysis. Volume 100:Issue 5(2021)
• Page Start: 1079
• Page End: 1095
• Publication Date: 2021-04-04
• Subjects: M. Mei; Convergence rate -- hyperbolic system of balance laws -- partial dissipation -- parabolic system -- stream function; 35B25 -- 35K45 -- 35L45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1634258
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : It is proved recently that partially dissipative hyperbolic systems converge globally-in-time to parabolic systems in a slow time scaling, when initial data are smooth and sufficiently close to constant equilibrium states. Based on this result, we establish error estimates between the smooth solutions of the hyperbolic systems of balance laws and those of the parabolic limit systems in one space dimension. The proof of the error estimates uses a stream function technique together with energy estimates. As applications of the results, we give five examples arising from physical models.