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The Equations of the Darcy–Brinkman Flow: the Lie Symmetry Classification, Conservation Laws, and Traveling Wave Solutions

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Abstract

We consider the differential equations that describe the Darcy–Brinkman flow. We provide the Lie symmetry classification of this system, construct conservation laws and study the system that describes the traveling wave solutions. We show that the integration of the last system is reducible to the Abel ordinary differential equation and indicate a case when this ordinary differential equation (ODE) is integrable in quadratures.

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REFERENCES

  1. H. C. Brinkman, ‘‘A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,’’ Appl. Sci. Res. 1, 27–34 (1949). https://doi.org/10.1007/BF02120313

    Article  MATH  Google Scholar 

  2. V. V. Lychagin and M. D. Roop, ‘‘Critical phenomena in filtration processes of real gases,’’ Lobachevskii J. Math. 41, 382–399 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  3. I. S. Krasil’shchik and O. I. Morozov, ‘‘The equation of filtration for real gases: Group classification, exact solutions, conservation laws, and differential invariants,’’ Lobachevskii J. Math. 43, 2781–2784 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khor’kova, I. S. Krasil’shchik, A. V. Samokhin, Yu. N. Torkhov, A. M. Verbovetsky, and A. M. Vinogradov, Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Vol. 182 of Transl. Math. Monogr. (Am. Math. Soc., Providence, 1999).

  5. E. Kamke, Differentialgleichungen. Lösungsmethoden und Lösungen. Band 1. Gewöhnliche Differentialgleichungen, 3rd ed. (Chelsea, New York, 1948).

  6. H. Baran and M. Marvan, Jets. A Software for Differential Calculus on Jet Spaces and Diffieties. http://jets.math.slu.cz/.

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ACKNOWLEDGMENTS

Computations were supported by the Jets software [6]. The authors are grateful to V. Lychagin for posing the problem and discussions.

Funding

The work of ISK was partially supported by the Russian Science Foundation Grant no. 21-71-20034.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997, Moscow, Russia

    I. S. Krasil’shchik & O. I. Morozov

Authors
  1. I. S. Krasil’shchik
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  2. O. I. Morozov
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Correspondence to I. S. Krasil’shchik or O. I. Morozov.

Additional information

(Submitted by A. M. Elizarov)

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Krasil’shchik, I.S., Morozov, O.I. The Equations of the Darcy–Brinkman Flow: the Lie Symmetry Classification, Conservation Laws, and Traveling Wave Solutions. Lobachevskii J Math 44, 3941–3944 (2023). https://doi.org/10.1134/S1995080223090160

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  • DOI: https://doi.org/10.1134/S1995080223090160

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