Center for Mathematical Analysis, Geometry and Dynamical Systems

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Publications

Mathematical investigations of a kinetic model for glycerol hydrogenolysis via heterogeneous catalysis

Publication . Costa, Fernando Pestana da; Ndlovu, Thandokuhle Quinton; Shozi, Mzamo

In this paper we report on some mathematical investigations of the chemical process for the hydrogenolysis of glycerol over a heterogeneous metal catalyst. The main interest of this process is related to the fact that glycerol is produced as a by-product in the production of biodiesel in huge amounts that are expected to exceed the projected demands. This makes the sustainability of biodiesel production depend on the conversion of the glycerol into useful products hence it is a desirable goal to have effective conversion methods. A reaction model from literature is used to derive a system of ordinary differential equations (ODE) which is then analysed using methods from qualitative analysis of ODEs. Numerical solutions of the system are simulated to try and find out the solution’s behaviour in the chemistry point of view. It was found that all solutions of the model converge to some stable limit point in a 2-dimensional plane in the positive cone of the R5 phase space, and the limit point depends on the values of rate constants ki as well as on the hydrogen to glycerol initial ratios. Even though the results are based on a specific kinetic model, it is hoped that they may help in providing tools for better understanding and description of the reaction.

2022-04Journal article

Open access

The continuous Redner–Ben-Avraham–Kahng coagulation system: well-posedness and asymptotic behaviour

Publication . Verma, Pratibha; Giri, Ankik Kumar; Costa, Fernando Pestana da

This paper examines the existence of solutions to the continuous Redner-Ben-Avraham-Kahng coagulation system under specific growth conditions on unbounded coagulation kernels at infinity. Moreover, questions related to uniqueness and continuous dependence on the data are also addressed under additional restrictions. Finally, the large-time behaviour of solutions is also investigated.

2023-03Journal article

Open access

Funding agency

Fundação para a Ciência e a Tecnologia

Funding programme

6817 - DCRRNI ID

Funding Award Number

UIDB/04459/2020