An application of semigroup theory to the coagulation-fragmentation models

Das A, Das N, Saha J (2021)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2021

Journal

Turkish Journal of Mathematics Scientific and Technical Research Council of Turkey

Book Volume: 45

Journal Issue: 5

DOI: 10.3906/mat-2101-114

Abstract

We present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.

Authors with CRIS profile

Arijit Das Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

National Institute of Technology, Tiruchirappalli (NIT Trichy) IN India (IN)

How to cite

APA:

Das, A., Das, N., & Saha, J. (2021). An application of semigroup theory to the coagulation-fragmentation models. Turkish Journal of Mathematics, 45(5). https://doi.org/10.3906/mat-2101-114

MLA:

Das, Arijit, Nilima Das, and Jitraj Saha. "An application of semigroup theory to the coagulation-fragmentation models." Turkish Journal of Mathematics 45.5 (2021).

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