Construction of global Riemann solutions with delta-type initial data for a thin film model with a perfectly soluble anti-surfactant solution

Li, Shuangrong; Shen, Chun

doi:10.1016/j.ijnonlinmec.2019.103392

Cited by 6 publications

(2 citation statements)

References 43 publications

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“…[36,62,65]). Similar concentration effects were also observed in a system modeling the polymer flooding of a porous medium [26], in pressureles gas dynamics [67] and in thin-film equations [40,59].…”

Section: Discussionsupporting

confidence: 67%

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

Kalisch

Mitrović

2022

Int. J. Appl. Comput. Math

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A weak notion of solution for systems of conservation laws in one dimension is put forward. In the framework introduced here, it can be shown that the Cauchy problem for any $$n\times n$$ n × n system of conservation laws has a solution. The solution concept is an extension of the notion of singular $$\delta $$ δ -shocks which have been used to provide solutions for Riemann problems in various systems, for example in cases where strict hyperbolicity or the genuine-nonlinearity condition are not satisfied, or in cases where initial conditions have large variation. We also introduce admissibility conditions which eliminate a wide range of unreasonable solutions. Finally, we provide an example from the shallow water system which justifies introduction of $$\delta $$ δ -distributions as a part of solutions to systems of conservation laws.

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Section: Discussionsupporting

confidence: 67%

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

Kalisch

Mitrović

2022

Int. J. Appl. Comput. Math

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“…In addition, it is well known that delta shock wave should be introduced in order to solve Riemann problems for some weak hyperbolic conservation systems and the theory of delta shock wave has been well established and developed in recent years, see [22][23][24][25][26][27][28] for examples. However, as far as we know, our constructed composite wave solution with the singularity of delta function cannot be found in any Riemann solution but only appears in the study [29][30][31] of wave interaction between a delta shock wave with a rarefaction wave for some hyperbolic systems of conservation laws.…”

Section: + P(ρ)mentioning

confidence: 99%

The Perturbed Riemann Problem for a Macroscopic Production Model with Chaplygin Gas

Wang

Shen

2020

Bull. Malays. Math. Sci. Soc.

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The exact Riemann solutions for a macroscopic production model under the equation of state given by the Chaplygin gas are solved explicitly for all possible Riemann initial data. It is discovered interestingly that a composite hyperbolic wave is involved in Riemann solution under some specially designated initial conditions, which is made up of a rarefaction wave and a delta contact discontinuity attached on the wave front of the rarefaction wave. Furthermore, the constructions of global solutions to the perturbed Riemann problem for this system are also displayed in completely explicit forms when the initial data are taken to be three piecewise constant states under some suitable restrictive conditions by using the method of characteristics. During the process of constructing global solutions, the interactions of elementary waves are studied in detail. Moreover, it is proved rigorously that Riemann solutions are stable with respect to the specific small perturbations of Riemann initial data.

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On the wave interactions for the drift-flux equations with the Chaplygin gas

Shen

2022

Monatsh Math

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Construction of global Riemann solutions with delta-type initial data for a thin film model with a perfectly soluble anti-surfactant solution

Cited by 6 publications

References 43 publications

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

On Existence and Admissibility of Singular Solutions for Systems of Conservation Laws

The Perturbed Riemann Problem for a Macroscopic Production Model with Chaplygin Gas

On the wave interactions for the drift-flux equations with the Chaplygin gas

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