Instantaneous gelation and non-existence of weak solutions for the Oort–Hulst–Safronov coagulation model-Reference-Cited by-同舟云学术

Instantaneous gelation and non-existence of weak solutions for the Oort–Hulst–Safronov coagulation model

Published:2023-02 Issue:2270 Volume:479 Page:
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Rai Pooja¹,Kumar Giri Ankik¹^ORCID,John Volker²³

Affiliation:

1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India

2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany

3. Department of Mathematics and Computer Science, Freie Universität of Berlin, Arnimallee 6, 14195 Berlin, Germany

Abstract

The possible occurrence of instantaneous gelation to the Oort–Hulst–Safronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the non-existence of mass-conserving weak solutions. Finally, it is shown that for such kernels, there is no weak solution to the OHS coagulation equation at any time interval.

Funder

Deutscher Akademischer Austauschdienst

Department of Science & Techonolgy (DST), India

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2022.0385

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