A global subsonic solution to an interacting transonic shock for the self-similar nonlinear wave equation
type: Item
instance of: scholarly article
title: A global subsonic solution to an interacting transonic shock for the self-similar nonlinear wave equation
zbMATH Open document ID: 1194.35262
author: Eun Heui Kim
published in: Journal of Differential Equations
publication date: 2010-06-25T00:00:00Z
review text: The existence of the subsonic solution to a two-dimensional Riemann problem governed by a self-similar nonlinear wave equation where the boundary of the subsonic region consists of a transonic shock and the sonic circle is presented. Thus the governing equation becomes a free boundary problem on the transonic shock and degenerates on the sonic circle. By utilizing the barrier methods and iterative methods, the well-posedness of the transonic shock in the entire subsonic region is shown and thus the global solution is established. This result does not rely on any smallness of Riemann data.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 76J20
zbMATH DE Number: 5726574
zbMATH Keywords: two-dimensional Riemann problem
zbMATH Keywords: transonic shock
zbMATH Keywords: sonic circle
MaRDI profile type: Publication
full work available at URL: j.jde.2010.02.021
OpenAlex ID: W1974909005
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DOI: 10.1016/J.JDE.2010.02.021
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description: scientific article; zbMATH DE number 5726574