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Global Existence and Mass Decay Analysis of solutions to the discrete Redner-Ben-Avraham-Kahng coagulation model

Pratibha Verma

Abstract

The Redner-Ben-Avraham-Kahng (RBK) coagulation model provide a fundamental framework for modeling the aggregation of particles in various physical and biological systems. In this paper, we investigate the global existence of solutions to the discrete version of RBK coagulation equations, encompassing a wide range of coagulation kernels. Furthermore, we demonstrate that the mass decays with time and will eventually reach to zero even if the original mass is not finite. A small size particle is produced in the RBK coagulation model when two large particles collide with a slight size difference. Dealing with the role played by large size particles in the creation of small size particles was the major challenge of this research.

Global Existence and Mass Decay Analysis of solutions to the discrete Redner-Ben-Avraham-Kahng coagulation model

Abstract

The Redner-Ben-Avraham-Kahng (RBK) coagulation model provide a fundamental framework for modeling the aggregation of particles in various physical and biological systems. In this paper, we investigate the global existence of solutions to the discrete version of RBK coagulation equations, encompassing a wide range of coagulation kernels. Furthermore, we demonstrate that the mass decays with time and will eventually reach to zero even if the original mass is not finite. A small size particle is produced in the RBK coagulation model when two large particles collide with a slight size difference. Dealing with the role played by large size particles in the creation of small size particles was the major challenge of this research.
Paper Structure (5 sections, 10 theorems, 51 equations)

This paper contains 5 sections, 10 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. Preliminaries
  4. Proof of Theorem \ref{['thm2.1']}
  5. Proof of Theorem \ref{['thm2.2']}

Key Result

Theorem 2.1

Let us assume ker1 holds along with either ker2 or ker3 for coagulation kernel $\theta_{i,j}$. For any initial data $f^{\text{in}}=(f_i^{\text{in}})_{i\ge 1} \in X_1^+$, the system drbk-drbkic has at least one solution $f$ on $[0, +\infty)$ which satisfies $f(t) \in X_1^+$ for each $t\in [0, +\infty

Theorems & Definitions (16)

  • Definition 2.1
  • Theorem 2.1
  • Theorem 2.2
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 4.1
  • ...and 6 more