Article
| Title: | Evolution of acceleration wave and interaction with a strong shock in a plasma with axial magnetic field and dust particles (English) |
| Author: | Palo, Nishi Deepa |
| Author: | Jena, Jasobanta |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 107-126 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The paper examines the evolution of a weak discontinuity, specifically, an acceleration wave in a one-dimensional unsteady plasma flow influenced by an axial magnetic field in the presence of dust particles. We obtained self-similar solutions through the application of Lie group transformations. This study also explores the idea of interaction between the acceleration wave and a strong shock wave, with particular emphasis on the roles played by dust particles and the magnetic field. The effects of various parameters involved in the flow are examined. Additionally, the reflected and transmitted waves following the interactions are analyzed and the results are depicted. (English) |
| Keyword: | compressible flow |
| Keyword: | quasilinear differential equation |
| Keyword: | shock wave |
| MSC: | 35L05 |
| MSC: | 35L72 |
| MSC: | 76N06 |
| MSC: | 76N30 |
| idZBL: | Zbl 08162248 |
| idMR: | MR5029291 |
| DOI: | 10.21136/AM.2026.0201-24 |
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| Date available: | 2026-02-02T12:03:40Z |
| Last updated: | 2026-03-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153336 |
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| Reference: | [1] Bluman, G. W., Cole, J. D.: Similarity Methods for Differential Equations.Applied Mathematical Sciences 13. Springer, New York (1974). Zbl 0292.35001, MR 0460846, 10.1007/978-1-4612-6394-4 |
| Reference: | [2] Chadha, M., Jena, J.: Self-similar solutions and converging shocks in a non-ideal gas with dust particles.Int. J. Non-Linear Mech. 65 (2014), 164-172. 10.1016/j.ijnonlinmec.2014.05.013 |
| Reference: | [3] Chadha, M., Jena, J.: Singular surface and steepening of waves in a non-ideal gas with dust particles.Comput. Appl. Math. 34 (2015), 729-739. Zbl 1357.76097, MR 3365685, 10.1007/s40314-014-0135-x |
| Reference: | [4] Clarke, J. F.: Small amplitude gasdynamic disturbances in an exploding atmosphere.J. Fluid Mech. 89 (1978), 343-356. Zbl 0396.76050, 10.1017/S0022112078002633 |
| Reference: | [5] Conforto, F.: Interaction between weak discontinuities and shocks in a dusty gas.J. Math. Anal. Appl. 253 (2001), 459-472. Zbl 0970.76101, MR 1808148, 10.1006/jmaa.2000.7152 |
| Reference: | [6] Jeffrey, A.: The propagation of weak discontinuities in quasi-linear hyperbolic systems with discontinuous coefficients. I. Fundamental theory.Appl. Anal. 3 (1973), 79-100. Zbl 0256.35054, MR 0393868, 10.1080/00036817308839058 |
| Reference: | [7] Jena, J.: Self-similar solutions in a plasma with axial magnetic field ($\theta$-pinch).Meccanica 47 (2012), 1209-1215. Zbl 1293.76180, MR 2924642, 10.1007/s11012-011-9505-2 |
| Reference: | [8] Jena, J., Chadha, M.: Interaction of acceleration wave with a strong shock is transient pinched plasma.J. Appl. Fluid Mech. 9 (2016), 2629-2634. 10.18869/acadpub.jafm.68.236.22847 |
| Reference: | [9] Jena, J., Singh, R.: Existence and interaction of acceleration wave with a characteristic shock in transient pinched plasma.Meccanica 48 (2013), 733-738. Zbl 1293.76080, MR 3032417, 10.1007/s11012-012-9627-1 |
| Reference: | [10] Kuwabara, S.: Similarity solutions for transient pinched plasma.J. Phys. Soc. Jap. 18 (1963), 713-718. 10.1143/JPSJ.18.713 |
| Reference: | [11] Lax, P. D.: Hyperbolic systems of conservation laws. II.Commun. Pure Appl. Math. 10 (1957), 537-566. Zbl 0081.08803, MR 0093653, 10.1002/cpa.3160100406 |
| Reference: | [12] Mentrelli, A., Ruggeri, T., Sugiyama, M., Zhao, N.: Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength.Wave Motion 45 (2008), 498-517. Zbl 1231.76130, MR 2406845, 10.1016/j.wavemoti.2007.09.005 |
| Reference: | [13] Morro, A.: Interaction of acoustic waves with shock waves in elastic solids.Z. angew. Math. Phys. 29 (1978), 822-827. Zbl 0387.76069, MR 0511914, 10.1007/BF01589293 |
| Reference: | [14] Pai, S. I., Hsieh, T.: Interaction terms in gas-solid two-phase flows.Z. Flugwiss. 21 (1973), 442-445. Zbl 0307.76059 |
| Reference: | [15] Palo, N. D., Jena, J., Chadha, M.: An analytical approach to study kinematics of shock waves in a dusty, cylindrical gas flow.ZAMM, Z. Angew. Math. Mech. 102 (2022), Article ID e202200019, 20 pages. Zbl 1536.76054, MR 4559166, 10.1002/zamm.202200019 |
| Reference: | [16] Pandey, M.: Evolution of weak discontinuities in non-ideal magnetogasdynamic equations.Int. J. Appl. Comput. Math. 1 (2015), 257-265. Zbl 1320.76125, MR 3346022, 10.1007/s40819-015-0033-y |
| Reference: | [17] Pandey, M., Sharma, V. D.: Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas.Wave Motion 44 (2007), 346-354. Zbl 1231.76132, MR 2311431, 10.1016/j.wavemoti.2006.12.002 |
| Reference: | [18] Radha, C., Sharma, V. D., Jeffrey, A.: On interaction of shock waves with weak discontinuities.Appl. Anal. 50 (1993), 145-166. Zbl 0739.76029, MR 1278323, 10.1080/00036819308840191 |
| Reference: | [19] Ruggeri, T.: Interaction between a discontinuity wave and a shock wave: Critical time for the fastest transmitted wave, example of the polytropic fluid.Appl. Anal. 11 (1980), 103-112. Zbl 0482.76062, MR 0599258, 10.1080/00036818008839323 |
| Reference: | [20] Sharma, V. D.: Quasilinear Hyperbolic Systems, Compressible Flows, and Waves.Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics 142. CRC Press, Boca Raton (2010). Zbl 1200.76002, MR 2668539, 10.1201/9781439836910 |
| Reference: | [21] Sharma, V. D., Ram, R., Sachdev, P. L.: Uniformly valid analytical solution to the problem of a decaying shock wave.J. Fluid Mech. 185 (1987), 153-170. Zbl 0651.76023, 10.1017/S0022112087003124 |
| Reference: | [22] Singh, R., Jena, J.: Interaction of an acceleration wave with a strong shock in reacting polytropic gases.Appl. Math. Comput. 225 (2013), 638-644. Zbl 1334.76138, MR 3129679, 10.1016/j.amc.2013.09.074 |
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