A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation

Prasanta Kumar Barik; Ankik Kumar Giri

doi:10.3934/krm.2018043

Article Contents

2018, Volume 11, Issue 5: 1125-1138. Doi: 10.3934/krm.2018043

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A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation

Prasanta Kumar Barik and
Ankik Kumar Giri^,

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India

* Corresponding author: A. K. Giri is supported by Faculty Initiation Grant: MTD/FIG/100680, Indian Institute of Technology Roorkee, Roorkee-247667, India
* Corresponding author: A. K. Giri is supported by Faculty Initiation Grant: MTD/FIG/100680, Indian Institute of Technology Roorkee, Roorkee-247667, India

Received: May 2017

Revised: October 2017

Published: May 2018

The first author is supported by University Grant Commission: 6405/11/44, India.

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Abstract

In general, the non-conservative approximation of coagulation-fragmentation equations (CFEs) may lead to the occurrence of gelation phenomenon. In this article, it is shown that the non-conservative approximation of CFEs can also provide the existence of mass conserving solutions to CFEs for large classes of unbounded coagulation and fragmentation kernels.

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Mathematics Subject Classification: Primary: 45K05, 45J05; Secondary: 34K30.

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References

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