# American Institute of Mathematical Sciences

April  2021, 14(2): 389-406. doi: 10.3934/krm.2021009

## 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

Received  March 2020 Revised  January 2021 Published  March 2021

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.

Citation: Prasanta Kumar Barik, Ankik Kumar Giri, Rajesh Kumar. Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates. Kinetic & Related Models, 2021, 14 (2) : 389-406. doi: 10.3934/krm.2021009
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