Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 182-201
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V. V. Palin. Limit Passage in the Construction of a Geometric Solution: The Case of a Rarefaction Wave. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 182-201. http://geodesic.mathdoc.fr/item/TM_2021_315_a12/
@article{TM_2021_315_a12,
author = {V. V. Palin},
title = {Limit {Passage} in the {Construction} of a {Geometric} {Solution:} {The} {Case} of a {Rarefaction} {Wave}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {182--201},
year = {2021},
volume = {315},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a12/}
}
TY - JOUR
AU - V. V. Palin
TI - Limit Passage in the Construction of a Geometric Solution: The Case of a Rarefaction Wave
JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY - 2021
SP - 182
EP - 201
VL - 315
UR - http://geodesic.mathdoc.fr/item/TM_2021_315_a12/
LA - ru
ID - TM_2021_315_a12
ER -
%0 Journal Article
%A V. V. Palin
%T Limit Passage in the Construction of a Geometric Solution: The Case of a Rarefaction Wave
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 182-201
%V 315
%U http://geodesic.mathdoc.fr/item/TM_2021_315_a12/
%G ru
%F TM_2021_315_a12
A method for constructing a geometric solution of the Riemann problem is described for a scalar conservation law perturbed by a rarefaction wave. The phase flow of the associated autonomous system is described topologically, and an explicit formula for the Hausdorff limit defining a geometric solution is presented.
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[3] P. D. Lax, Hyperbolic Partial Differential Equations, Courant Lect. Notes Math., 14, Am. Math. Soc., Providence, RI, 2006 | DOI
[4] Palin V.V., “Konstruktsiya geometricheskogo resheniya v sluchae volny razrezheniya”, Zap. nauchn. sem. POMI, 489, 2020, 55–66 | MR
[5] V. V. Palin, “On the passage to the limit in the construction of geometric solutions of the Riemann problem”, Math. Notes, 108:3–4 (2020), 356–369 | DOI | MR
