Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates

Prasanta Kumar Barik; Ankik Kumar Giri; Rajesh Kumar

doi:10.3934/krm.2021009

Article Contents

2021, Volume 14, Issue 2: 389-406. Doi: 10.3934/krm.2021009

This issue Previous Article Projective integration schemes for hyperbolic moment equations Next Article

Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates

1.
Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore-560065, Karnataka, India
2.
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India
3.
Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani-333031, Rajasthan, India

^* Corresponding author: Prasanta Kumar Barik
^* Corresponding author: Prasanta Kumar Barik

Received: March 2020

Revised: January 2021

Early access: March 2021

Published: April 2021

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Abstract

In this article, the existence of mass-conserving solutions is investigated to the continuous coagulation and collisional breakage equation with singular collision kernels. Here, the probability distribution function attains singularity near the origin. The existence result is constructed by using both conservative and non-conservative truncations to the continuous coagulation and collisional breakage equation. The proof of the existence result relies on a classical weak $ L^1 $ compactness method.

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Mathematics Subject Classification: Primary: 45K05; Secondary: 34K30.

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