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Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property

Author

Listed:
  • Md. Sahidul Islam

    (Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, Japan
    Department of Mathematical and Physical Sciences, East West University, Dhaka 1212, Bangladesh)

  • Masato Kimura

    (Faculty of Mathematics and Physics, Kanazawa University, Kanazawa 920-1192, Japan)

  • Hisanori Miyata

    (Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, Japan)

Abstract

In this paper, we develop a generalized moment method with a continuous weight function for the Smoluchowski coagulation equation in its continuous form to study the mass conservation property of this equation. We first establish some basic inequalities for the generalized moment and prove the mass conservation property under a sufficient condition on the kernel and an initial condition, utilizing these inequalities. Additionally, we provide some concrete examples of coagulation kernels that exhibit mass conservation properties and show that these kernels exhibit either polynomial or exponential growth along specific particular curves.

Suggested Citation

  • Md. Sahidul Islam & Masato Kimura & Hisanori Miyata, 2023. "Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2770-:d:1174665
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