### Abstract

We study the enzymatic degradation of xenobiotic polymers mathematically. As a mathematical model, we derive a linear second-order hyperbolic partial differential equation which governs the evolution of the weight distribution with respect to the molecular weight. Given an initial weight distribution and a final weight distribution, we formulate a problem to determine a degradation rate. We establish a necessary and sufficient condition for which the problem has a local solution. We also introduce a numerical technique based on our analysis, and present a numerical result that we obtained applying weight distributions before and after enzymatic degradation of polyvinyl alcohol.

Original language | English |
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Pages (from-to) | 1497-1514 |

Number of pages | 18 |

Journal | Applied Mathematical Modelling |

Volume | 30 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2006 |

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### Keywords

- Enzymatic random depolymerization
- Hyperbolic partial differential equation
- Mathematical model
- Numerical simulation
- Polyvinyl alcohol

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Control and Optimization

### Cite this

*Applied Mathematical Modelling*,

*30*(12), 1497-1514. https://doi.org/10.1016/j.apm.2005.12.011