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Methods for Solving the Problem of Zonal Electrophoresis with Periodic Initial Data

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Abstract

We consider the problem of zonal electrophoresis of a two-component mixture with spatially periodic initial distribution of the mixture components. Two methods of solution are proposed: analytical (hodograph method) and numerical (method of finite volumes). A comparative analysis of the results obtained is performed.

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References

  1. E. T. Copson, “On the Riemann–Green function,” Arch. Rat. Mech. Anal., 1, 324–348 (1958).

  2. T. F. Dolgikh, “Solution of the problem of mass transfer under the action of an electric field in a two-component mixture,” Izv. Sev.-Kavkaz. Nauch. Tsentr. Vyssh. Shkoly. Estestv. Nauki., No. 3-1 (195-1), 28–35 (2017).

    Google Scholar 

  3. Dolgikh T. F., Zhukov M. Yu., Shiryaeva E. V., “Solution of elliptic equations with periodic data for the problem of zonal electrophoresis,” Vestn. Voronezh. Univ. Ser. Fiz. Mat., No. 2, 85–96 (2017).

  4. T. F. Dolgikh, “Method of finite volumes for solving problems of zonal electrophoresis,” in: XIX Int. Conf. “Modern problems of continuum mechanics” (Rostov-on-Don, October 15–18, 2018) (2018), pp. 94–98.

  5. A. Harten, “High resolution schemes for hyporbolic conservation laws,” J. Comput. Phys., 135 (1997), pp. 260–278.

    Article  MATH  Google Scholar 

  6. B. L. Rozhdestvensky and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1978).

  7. S. I. Senashov and A. Yakhno, “Conservation laws, hodograph transformation, and boundary-value problems of plane plasticity,” SIGMA., 8 (2012).

  8. S. K. Zhdanov and B. A. Trubnikov, Qusi-Gas Unstable Media [in Russian], Nauka, Moscow (1971).

  9. M. Yu. Zhukov, Mass Transfer by Electric Fields [in Russian], Rostov-on-Don (2005).

  10. M. Yu. Zhukov and E. V. Shiryaeva, Mathematical Modeling of the Process of Impurity Sedimentation in Liquid Flows [in Russian], Rostov-on-Don (2016).

  11. M. Yu. Zhukov, E. V. Shiryaeva, and T. F. Dolgikh, Hodograph method for solving hyperbolic and elliptic quasilinear equations [in Russian], Rostov-on-Don (2015).

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Correspondence to T. F. Dolgikh.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.

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Dolgikh, T.F. Methods for Solving the Problem of Zonal Electrophoresis with Periodic Initial Data. J Math Sci 267, 706–715 (2022). https://doi.org/10.1007/s10958-022-06164-5

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  • DOI: https://doi.org/10.1007/s10958-022-06164-5

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