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October  2018, 11(5): 1125-1138. doi: 10.3934/krm.2018043

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

 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

Received  May 2017 Revised  October 2017 Published  May 2018

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

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.

Citation: Prasanta Kumar Barik, Ankik Kumar Giri. A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation. Kinetic & Related Models, 2018, 11 (5) : 1125-1138. doi: 10.3934/krm.2018043
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##### References:
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