Methods and Applications of Analysis

Volume 28 (2021)

Number 4

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part III

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Hsiao–Liu correction functions and their applications

Pages: 487 – 506

DOI: https://dx.doi.org/10.4310/MAA.2021.v28.n4.a5

Authors

Hongyun Peng (School of Applied Mathematics, Guangdong University of Technology, Guangzhou, China)

Changjiang Zhu (School of Mathematics, South China University of Technology, Guangzhou, China)

Abstract

In [19], Hsiao–Liu correction functions were first introduced to show that the solutions of a system of hyperbolic conservation laws with damping time asymptotically tend to the nonlinear diffusion waves governed by the classical Darcy’s law. This is a survey paper on Hsiao–Liu correction functions and their applications.

Keywords

correction functions, nonlinear diffusion waves, Darcy’s law, asymptotic stability

2010 Mathematics Subject Classification

35B40, 35B45, 35L60, 35L65

Full Text (PDF format)

The research of H.Y. Peng was supported by the National Natural Science Foundation of China (No. 11901115), Natural Science Foundation of Guangdong Province (No. 2019A1515010706).

C.J. Zhu was supported by the National Natural Science Foundation of China (No. 11771150, 11831003 and 11926346).

Received 26 March 2020

Accepted 17 June 2020

Published 10 June 2022