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An application of semigroup theory to the pure fragmentation equation

  • Proceedings: ICMAA 2016
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Abstract

The present work deals with the mathematical analysis of the population balance equation involving pure fragmentation using the semigroup theory of linear operators. The existence and uniqueness of non-negative, strong solution is established.

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References

  1. Edwards, B.F., M. Cai, and H. Han. 1990. Rate equation and scaling for fragmentation with mass loss. Physical Review A 41(10):5755.

    Article  Google Scholar 

  2. Aizenman, M., and T.A. Bak. 1979. Convergence to equilibrium in a system of reacting polymers. Communications in Mathematical Physics 65(3):203–230.

    Article  MathSciNet  Google Scholar 

  3. Melzak, Z. 1957. A scalar transport equation. Transactions of American Mathematical Society 85(2):547–560.

    Article  MathSciNet  Google Scholar 

  4. Stewart, I.W. 1989. A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels. Mathematical Methods in the Applied Sciences 11(5):627–648.

    Article  MathSciNet  Google Scholar 

  5. Stewart, I.W. 1990. A uniqueness theorem for the coagulation-fragmentation equation. Mathematical Proceedings of the Cambridge Philosophical Society 107:573–578.

  6. McLaughlin, D.J., W. Lamb, and A. McBride. 1997. A semigroup approach to fragmentation models. SIAM Journal on Mathematical Analysis 28(5):1158–1172.

    Article  MathSciNet  Google Scholar 

  7. McGrady, E., and R.M. Ziff. 1987. Shattering transition in fragmentation. Physical review letters 58(9):892.

    Article  MathSciNet  Google Scholar 

  8. Ziff, R.M., and E. McGrady. 1985. The kinetics of cluster fragmentation and depolymerisation. Journal of Physics A: Mathematical and General 18(15):3027.

    Article  MathSciNet  Google Scholar 

  9. Ziff, R.M., and E. McGrady. 1986. Kinetics of polymer degradation. Macromolecules 19(10):2513–2519.

    Article  Google Scholar 

  10. Giri, A.K., P. Laurencot, and G. Warnecke. 2012. Weak solutions to the continuous coagulation equation with multiple fragmentation. Nonlinear Analysis: Theory, Methods & Applications 75(4):2199–2208.

    Article  MathSciNet  Google Scholar 

  11. Pazy, A. 2012. Semigroups of linear operators and applications to partial differential equations, Vol. 44. Springer Science & Business Media.

  12. Pryce, J.D. 2014. Basic methods of linear functional analysis, Courier Corporation.

  13. Hille, E., Phillips, R.S. 1996. Functional analysis and semi-groups, Vol. 31. American Mathematical Society.

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Authors and Affiliations

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

    Nilima Das, Jitraj Saha & Jitendra Kumar

Authors
  1. Nilima Das
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  2. Jitraj Saha
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  3. Jitendra Kumar
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Corresponding author

Correspondence to Nilima Das.

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Funding

The authors (ND and JS) are thankful to Ministry of Human Resources and Development, Government of India, for their financial support during this work.

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The authors give their consent for publication. There is no any conflict of interest involved.

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This paper does not contain any studies with animals performed by any of the authors.

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Das, N., Saha, J. & Kumar, J. An application of semigroup theory to the pure fragmentation equation. J Anal 28, 95–106 (2020). https://doi.org/10.1007/s41478-017-0045-6

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  • DOI: https://doi.org/10.1007/s41478-017-0045-6

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