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On the global solutions of discrete Safronov–Dubovskiǐ aggregation equation

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Abstract

In this article, the existence and uniqueness of global solutions to the discrete Safronov–Dubovskiǐ aggregation equation is studied. The unbounded aggregation kernel exhibits at most linear growth at infinity. The solution exhibits mass conservation property without any further restriction over the kernels.

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References

  1. Bagland, V.: Convergence of a discrete Oort–Hulst–Safronov equation. Math. Methods Appl. Sci. 28(13), 1613–1632 (2005)

    Article  MathSciNet  Google Scholar 

  2. Ball, J.M., Carr, J., Penrose, O.: The Becker–Döring cluster equations: basic properties and asymptotic behaviour of solutions. Commun. Math. Phys. 104(4), 657–692 (1986)

    Article  Google Scholar 

  3. Brezis,H.: Functional analysis, Sobolev spaces and partial differential equations. Springer (2010)

  4. Davidson, J.: Existence and uniqueness theorem for the Safronov-Dubovskiǐ coagulation equation. Zeitschrift für angewandte Mathematik und Physik 65(4), 757–766 (2014)

    Article  MathSciNet  Google Scholar 

  5. Dubovskiǐ, P.B.: Structural stability of disperse systems and finite nature of a coagulation front. J. Experim. Theor. Phys. 89(2), 384–390 (1999)

  6. Dubovskiǐ, P.B.: A ‘triangle’ of interconnected coagulation models. J. Phys. A: Math. Gen. 32(5), 781 (1999)

  7. Kreyszig, E.: Introductory functional analysis with applications, vol. 1. Wiley, New York (1978)

    MATH  Google Scholar 

  8. Lachowicz, M., Laurençot, P., Wrzosek, D.: On the Oort–Hulst–Safronov coagulation equation and its relation to the Smoluchowski equation. SIAM J. Math. Anal. 34(6), 1399–1421 (2003)

    Article  MathSciNet  Google Scholar 

  9. Laurençot, P.: Convergence to self-similar solutions for a coagulation equation. Zeitschrift für angewandte Mathematik und Physik 56(3), 398–411 (2005)

    Article  MathSciNet  Google Scholar 

  10. Oort, J.H., Van de Hulst, H.C.: Gas and smoke in interstellar space. Bull. Astronom. Inst. Netherlands 10, 187 (1946)

    Google Scholar 

  11. Safronov,VS.: Evolution of the protoplanetary cloud and formation of the earth and the planets. Israel Program for Scientific Translations (1972)

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

    Google Scholar 

  13. Wattis, J.A.D.: A coagulation-disintegration model of Oort–Hulst cluster-formation. J. Phys. A: Math. Theor. 45(42), 425001 (2012)

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Acknowledgements

The authors are thankful to the anonymous reviewers for providing valuable suggestions which have helped to prove proposition 2.1 in brief manner and also enhance the quality of the manuscript.

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  1. Department of Mathematics, National Institute of Technology Tiruchirappalli, Tiruchirappalli, Tamil Nadu, 620 015, India

    Arijit Das & Jitraj Saha

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  1. Arijit Das
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  2. Jitraj Saha
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Correspondence to Jitraj Saha.

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AD thanks Ministry of Education (MoE), Govt. of India for their funding support during his PhD program. JS thanks NITT for their support through seed Grant (file no.: NITT / R & C / SEED GRANT / 19 - 20 / P - 13 / MATHS / JS / E1) during this work.

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Das, A., Saha, J. On the global solutions of discrete Safronov–Dubovskiǐ aggregation equation. Z. Angew. Math. Phys. 72, 183 (2021). https://doi.org/10.1007/s00033-021-01612-9

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  • DOI: https://doi.org/10.1007/s00033-021-01612-9

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