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Existence of Solutions of the third term of the Connaughton-Newell Model with a source term

Anh Viet Nguyen

Abstract

The Connaughton-Newell equation is an approximation of three-wave kinetic equations using a fully non-linear coagulation-fragmentation model. This equation consists of three non-linear operators. In this paper, we proved that assuming a constant interaction kernel and a well-behaved source term, the third operator of the Connaughton-Newell equation has a solution.

Existence of Solutions of the third term of the Connaughton-Newell Model with a source term

Abstract

The Connaughton-Newell equation is an approximation of three-wave kinetic equations using a fully non-linear coagulation-fragmentation model. This equation consists of three non-linear operators. In this paper, we proved that assuming a constant interaction kernel and a well-behaved source term, the third operator of the Connaughton-Newell equation has a solution.
Paper Structure (2 sections, 4 theorems, 38 equations)

This paper contains 2 sections, 4 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem 1

Key Result

Theorem 1

Assuming that (A1)--(A4) hold, then equation eq2 admits at least one solution.

Theorems & Definitions (8)

  • Theorem 1
  • Remark 2
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof