An Informal Account of Recent Results on Initial-Boundary Value Problems for Systems of Conservation Laws
Year: 2024
Author: Laura V. Spinolo, Fabio Ancona, Andrea Marson
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 349–368
Abstract
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [F. Ancona et al. ArXiv: 2401.14865], where new global-in-time existence results for admissible solutions of nonlinear systems of conservation laws defined in domains with boundaries are established. The main novelty of that work is that the solution is constructed by taking into account the underlying viscous mechanism, which is relevant because, in the case of initial-boundary value problems, different viscous approximations yield in general different limits. In the present note we will frame the analysis of the paper mentioned in the relevant context, compare the main result with the previous existing literature, and touch upon the most innovative technical points of the proof.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0014
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 349–368
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Systems of conservation laws initial-boundary value problems hyperbolic systems wave front-tracking boundary characteristic case mixed hyperbolic-parabolic systems boundary layers.