Skip to main content
SpringerLink
Log in

Existence of Equilibrium Solution of the Coagulation–Fragmentation Equation with Linear Fragmentation Kernel

  • Conference paper
  • First Online:
Mathematics and Computing (ICMC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 253))

Included in the following conference series:

  • 653 Accesses

Abstract

The existence of equilibrium solution of a coagulation–fragmentation equation is shown in this article. We study the problem for a linear fragmentation kernel. A numerical example is provided to explore the given investigation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aizenman, M., Bak, T.A.: Convergence to equilibrium in a system of reacting polymers. Commun. Math. Phys. 65(3), 203–230 (1979)

    Article  MathSciNet  Google Scholar 

  2. Barrow, J.D.: Coagulation with fragmentation. J. Phys. A Math. Gen. 14(3), 729 (1981)

    Article  MathSciNet  Google Scholar 

  3. Drake, R.L.: A general mathematical survey of the coagulation equation. Top. Curr. Aerosol Res. (Part 2) 3, 201–376 (1972)

    Google Scholar 

  4. Dubovskiǐ, P., Galkin, V.A., Stewart, I.W.: Exact solutions for the coagulation-fragmentation equation. J. Phys. A Math. Gen. 25(18), 4737 (1992)

    Article  MathSciNet  Google Scholar 

  5. Dubovskiǐ, P., Stewart, I.W.: Trend to equilibrium for the coagulation-fragmentation equation. Math. Methods Appl. Sci. 19(10), 761–772 (1996)

    Article  MathSciNet  Google Scholar 

  6. Edwards, R.: Functional analysis: theory and applications, Holt, Rinehart and Winston, New York, 1965. MR 36, 4308 (1994)

    Google Scholar 

  7. Kumar, J., Kaur, G., Tsotsas, E.: An accurate and efficient discrete formulation of aggregation population balance equation. Kinet. Relat. Models 9(2), 373–391 (2016)

    Article  MathSciNet  Google Scholar 

  8. Kumar, J., Saha, J., Tsotsas, E.: Development and convergence analysis of a finite volume scheme for solving breakage equation. SIAM J. Numer. Anal. 53(4), 1672–1689 (2015)

    Article  MathSciNet  Google Scholar 

  9. Okubo, A.: Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Adv. Biophys. 22, 1–94 (1986)

    Article  Google Scholar 

  10. Perelson, A.S., Samsel, R.W.: Kinetics of red blood cell aggregation: an example of geometric polymerization. In: Kinetics of Aggregation and Gelation, pp. 137–144 (1984)

    Chapter  Google Scholar 

  11. Safronov, V.S. Evolution of the protoplanetary cloud and formation of the earth and planets. In: Safronov, V.S. (ed.) Evolution of the Protoplanetary Cloud and Formation of the Earth and Planets, vol. 1, 212 p. Translated from Russian. Israel Program for Scientific Translations, Keter Publishing House, Jerusalem, Israel (1972)

    Google Scholar 

  12. Smoluchowski, M.: Drei vortrage uber diffusion. brownsche bewegung und koagulation von kolloidteilchen. Z. Phys. 17, 557–585 (1916)

    Google Scholar 

  13. Smoluchowski, M.: Grundriß der koagulationskinetik kolloider lösungen. Colloid Polym. Sci. 21(3), 98–104 (1917)

    Google Scholar 

  14. Stewart, I.W., Dubovskiǐ, P.: Approach to equilibrium for the coagulation-fragmentation equation via a Lyapunov functional. Math. Methods Appl. Sci. 19(3), 171–185 (1996)

    Article  MathSciNet  Google Scholar 

  15. Stewart, I.W., Meister, E.: A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels. Math. Methods Appl. Sci. 11(5), 627–648 (1989)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, West Bengal, India

    Debdulal Ghosh & Jitendra Kumar

Authors
  1. Debdulal Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jitendra Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Debdulal Ghosh .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  2. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Debasis Giri

  3. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Ram N. Mohapatra

  4. Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  5. Uşak University, Uşak, Turkey

    Ekrem Savas

  6. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Tanmoy Som

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ghosh, D., Kumar, J. (2018). Existence of Equilibrium Solution of the Coagulation–Fragmentation Equation with Linear Fragmentation Kernel. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_23

Download citation

Publish with us

Policies and ethics

Search

Navigation