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Convergence rates of vanishing diffusion limit on conservative form of Hsieh's equation
Author(s) -
Fan Long,
Toureche Trouba Nafissa
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12366
Subject(s) - mathematics , sobolev space , diffusion , convergence (economics) , limit (mathematics) , nonlinear system , mathematical analysis , zero (linguistics) , initial value problem , cauchy distribution , rate of convergence , diffusion equation , physics , computer science , computer network , linguistics , philosophy , channel (broadcasting) , quantum mechanics , economics , thermodynamics , economic growth , economy , service (business)
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.