Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves

Sil, Subhankar; Sekhar, T. Raja

doi:10.1016/j.jmaa.2020.124847

Cited by 26 publications

(10 citation statements)

References 33 publications

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“…More specifically, the singular δ-standing wave was found by Sun [39] when the Riemann problem for (1.1) was considered under the situation p(ρ) = ρ. Furthermore, some new exact solutions for (1.1) in the case of p(ρ) = ρ have also been obtained by Sil and Raja Sekhar [37,38] with the help of nonclassical symmetry analysis as well as interactions of nonlinear waves have been widely investigated by Minhajul and Raja Sekhar [21]. Very recently, exact Riemann solutions have been obtained and wave interactions have been dealt with carefully in [43] for (1.1) by taking the pressure-density relation p(ρ) = − 1 ρ for Chaplygin gas.…”

Section: Introductionmentioning

confidence: 80%

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

Shan

Shen²,

Wei³

2022

Math. Model. Nat. Phenom.

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The exact Riemann solutions for the extended macroscopic production model with an adiabatic exponent are constructed in perfectly explicit forms. The asymptotic limit of Riemann solution consisting of 1-shock wave and 2-contact discontinuity tends to a delta shock solution for the pressureless gas dynamics model under the special over-compressive entropy condition as the adiabatic exponent drops to one. In contrast, the asymptotic limit of Riemann solution composed of 1-rarefaction wave and 2-contact discontinuity tends to the vacuum solution surrounded by two contact discontinuities by letting the adiabatic exponent tend to one, in which the state in the interior of the 1-rarefaction wave fan is developed into vacuum. The intrinsic phenomena of concentration and cavitation are identified and investigated carefully during this limiting process, which displays more complicated and completely different behavior compared with previous literature. In addition, some representative numerical calculations are also provided, which are in well agreement with our theoretical results.

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Section: Introductionmentioning

confidence: 80%

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

Shan

Shen²,

Wei³

2022

Math. Model. Nat. Phenom.

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“…Very recently, the interactions of nonlinear waves for this macroscopic production model have also been investigated carefully by Manhajul and Raja Sekhar 35 with the help of the hodograph transformation in connection with the technique of differential constraints. Also see Sil and Raja Sekhar 36,37 about the symmetry analysis of this model (). Hence, it is natural and also necessary to investigate the limits of Riemann solutions for the perturbed macroscopic production model for the actual comparisons of dynamical behaviors among different macroscopic production models.…”

Section: Introductionmentioning

confidence: 99%

The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model

Zhang

Sun

2021

Math Methods in App Sciences

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The exact solutions of the Riemann problems for the two different perturbed macroscopic production models are considered and constructed, respectively, for all the possible cases. It is found that the asymptotic limits of solutions to the Riemann problem for the first kind of perturbed macroscopic production model do not converge to those of the pressureless gas dynamics model, because the delta shock wave in the limiting situation has different propagation speed and strength from those for the pressureless gas dynamics model. In order to remedy it, the second kind of perturbed macroscopic production model is proposed, whose asymptotic limits of Riemann solutions are identical with those of the pressureless gas dynamics model.

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“…17 For the exact solution of PDEs arising in many physical phenomena, using symmetry analysis and Riemann problem, we refer Bira et al 18,21 and Sahoo et al, 19,20 whereas the evolutionary behavior of weak discontinuities and elementary wave interaction for quasi-linear hyperbolic systems, we refer Raja et al, 22 Satapathy and Sekhar, 23 Zeidan and Bira, 24 and Sil and Raja Sekhar. 25 The structure of this article is as follows: Section 2 deals with a brief discussion on the model along with the derivation of the symmetry group of transformations. The construction of optimal algebras using the commutative table, adjoint table, and their classification are discussed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Study of wave propagation in arterial blood flow under symmetry analysis

Shagolshem

Bira

Zeidan

2022

Math Methods in App Sciences

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In this paper, we address a one-dimensional quasi-linear hyperbolic system of equations describing blood flow through compliant axi-symmetric vessels. From the symmetry analysis, we derive symmetry group of transformations and the corresponding symmetry generators by analyzing the parameters. Next, with the help of symmetry generators and invariant functions, we construct and classify the optimal system of subalgebras. Further, we obtained the similarity variables and similarity forms for each subalgebra leading to the reduction of the given governing coupled PDEs to the system of ODEs. Moreover, we studied the nature of blood flow velocity as well as the cross-sectional area of the arteries under the influence of arterial stiffness s graphically. Finally, the evolutionary behavior of weak discontinuity in the blood flow pattern is discussed with respect to aging.

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Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves

Cited by 26 publications

References 33 publications

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

The adiabatic exponent limits of Riemann solutions for the extended macroscopic production model

The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model

Study of wave propagation in arterial blood flow under symmetry analysis

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