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References (32)
-
A. Bressan (1992)
Global solutions of systems of conservation laws by wave-front trackingJournal of Mathematical Analysis and Applications, 170
-
B. François, James François (1999)
Duality solutions for pressureless gases, monotone scalar conservation laws, and uniquenessCommunications in Partial Differential Equations, 24
-
H. Holden, N. Risebro (2002)
Front Tracking for Hyperbolic Conservation Laws -
A. Bressan (1999)
Hyperbolic Systems of Conservation LawsRevista Matematica Complutense, 12
-
Fabio Cavalletti, M. Sedjro, Michael Westdickenberg (2013)
A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics EquationsSIAM J. Math. Anal., 47
-
Y. Brenier, E. Grenier (1998)
Sticky Particles and Scalar Conservation LawsSIAM Journal on Numerical Analysis, 35
-
Mathematisches Oberwolfach, C. Dafermos, Randy LeVeque (2004)
Hyperbolic Conservation LawsOberwolfach Reports, 5
-
M. Nedeljkov (2014)
Higher order shadow waves and delta shock blow up in the Chaplygin gasJournal of Differential Equations, 256
-
J. Conway (2012)
A Course in Abstract Analysis -
P. Floch (1990)
An existence and uniqueness result for two nonstrictly hyperbolic systems -
M. Nedeljkov (2010)
Shadow Waves: Entropies and Interactions for Delta and Singular ShocksArchive for Rational Mechanics and Analysis, 197
-
F. Huang, Zhen Wang (2001)
Well Posedness for Pressureless FlowCommunications in Mathematical Physics, 222
-
Wancheng Sheng, Tong Zhang (1999)
The Riemann Problem for the Transportation Equations in Gas Dynamics -
C. Dafermos (1973)
The entropy rate admissibility criterion for solutions of hyperbolic conservation lawsJournal of Differential Equations, 14
-
(2020)
Energy dissipation admissibility condition for shadow waves, preprint -
Luca Natile, Giuseppe Savaré (2009)
A Wasserstein Approach to the One-Dimensional Sticky Particle SystemSIAM J. Math. Anal., 41
-
Truyen Nguyen, A. Tudorascu (2015)
One-Dimensional Pressureless Gas Systems with/without ViscosityCommunications in Partial Differential Equations, 40
-
B. Keyfitz (2011)
SINGULAR SHOCKS: RETROSPECTIVE AND PROSPECTIVEConfluentes Mathematici, 03
-
M. Mazzotti (2009)
Nonclassical Composition Fronts in Nonlinear Chromatography: Delta-ShockIndustrial & Engineering Chemistry Research, 48
-
M. Sun (2013)
Interactions of delta shock waves for the chromatography equationsAppl. Math. Lett., 26
-
B. Keyfitz, H. Kranzer (1995)
SPACES OF WEIGHTED MEASURES FOR CONSERVATION LAWS WITH SINGULAR SHOCK SOLUTIONSJournal of Differential Equations, 118
-
N. Risebro (1993)
A front-tracking alternative to the random choice method, 117
-
Camillo Lellis, L. Székelyhidi (2007)
On Admissibility Criteria for Weak Solutions of the Euler EquationsArchive for Rational Mechanics and Analysis, 195
-
Chun-fang Shen (2015)
The Riemann problem for the pressureless Euler system with the Coulomb-like friction termIma Journal of Applied Mathematics, 81
-
A. Meurman, M. Primc (1998)
Annihilating fields of standard modules of sl(2, C)~ and combinatorial identiesMemoirs of the American Mathematical Society, 137
-
Camillo Lellis (2008)
Rectifiable Sets, Densities and Tangent Measures -
M. Nedeljkov, Sanja Ružičić (2017)
On the uniqueness of solution to generalized Chaplygin gasDiscrete and Continuous Dynamical Systems, 37
-
C. Dafermos (2000)
Hyberbolic Conservation Laws in Continuum Physics -
E. Weinan, Y. Rykov, Y. Sinai (1996)
Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamicsCommunications in Mathematical Physics, 177
-
Dalal Daw, M. Nedeljkov (2016)
Shadow waves for pressureless gas balance lawsAppl. Math. Lett., 57
-
M. Nedeljkov (2004)
Delta and singular delta locus for one‐dimensional systems of conservation lawsMathematical Methods in the Applied Sciences, 27
-
L. Boudin (2000)
A Solution with Bounded Expansion Rate to the Model of Viscous Pressureless GasesSIAM J. Math. Anal., 32
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2020
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-020-00377-z
- Publisher site
- See Article on Publisher Site
Abstract
In this paper the new procedure for a construction of an approximated solution to initial data problem for one-dimensional pressureless gas dynamics system is introduced. The procedure is based on solving the Riemann problems and tracking singular wave interactions. For that system the new problem with initial data containing Dirac delta function is solved whenever two waves interact. Use of the shadow waves as singular solutions to such problems enables us to easily solve the interaction problems. That permits us to make a simple extension of the well known Wave Front Tracking algorithm. A non-standard part of the new algorithm is dealing with delta functions as a part of a solution. In the final part of the paper we show that the approximated solution has a subsequence converging to a signed Radon measure.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 15, 2020