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OverviewThe authors study the perturbation of a shock wave in conservation laws with physical viscosity. They obtain the detailed pointwise estimates of the solutions. In particular, they show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small but independent. The authors' assumptions on the viscosity matrix are general so that their results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. The authors' analysis depends on accurate construction of an approximate Green's function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that the author can close the nonlinear term through Duhamel's principle. Full Product DetailsAuthor: Tai-Ping Liu , Yanni ZengPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 234/1105 Weight: 0.266kg ISBN: 9781470410162ISBN 10: 1470410168 Pages: 168 Publication Date: 30 June 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction Preliminaries Green's functions for systems with constant coefficients Green's function for systems linearized along shock profiles Estimates on Green's function Estimates on crossing of initial layer Estimates on truncation error Energy type estimates Wave interaction Stability analysis Application to magnetohydrodynamics BibliographyReviewsAuthor InformationTai-Ping Liu, Institute of Mathematics, Academia Sinica, Taipei, Taiwan, and Stanford University, CA, USA. Yanni Zeng, University of Alabama at Birmingham, AL, USA. Tab Content 6Author Website:Countries AvailableAll regions |