Convergence rates of vanishing diffusion limit on conservative form of Hsieh's equation. Issue 3 (13th January 2021)

• Record Type: Journal Article
• Authors: Fan, Long; Toureche Trouba, Nafissa
• Is Part Of: Studies in applied mathematics. Volume 146:Issue 3(2021)
• Page Start: 753
• Page End: 776
• Publication Date: 2021-01-13
• Subjects: conservative form -- Hsieh's equations -- diffusion waves -- global unique solvability -- vanishing diffusion limit; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12366
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: The aim of this paper is to study the global unique solvability on Sobolev solution perturbated around diffusion waves to the Cauchy problem of conservative form of Hsieh's equations. Furthermore, convergence rates are also obtained as one of the diffusion parameters goes to zero. The difficulty is created due to conservative nonlinearity to enclose the uniform (in diffusion parameter) higher order energy estimates. However this kind of difficulty will not occur for both the nonconservative nonlinearity and fixed diffusion parameter. The more subtle mathematical analysis needs to be introduced to overcome the difficulties.