### 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 |
---|---|

Pages (from-to) | 1497-1514 |

Number of pages | 18 |

Journal | Applied Mathematical Modelling |

Volume | 30 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2006 |

### Fingerprint

### 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

**Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers.** / Watanabe, Masaji; Kawai, Fusako.

Research output: Contribution to journal › Article

*Applied Mathematical Modelling*, vol. 30, no. 12, pp. 1497-1514. https://doi.org/10.1016/j.apm.2005.12.011

}

TY - JOUR

T1 - Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers

AU - Watanabe, Masaji

AU - Kawai, Fusako

PY - 2006/12

Y1 - 2006/12

N2 - 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.

AB - 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.

KW - Enzymatic random depolymerization

KW - Hyperbolic partial differential equation

KW - Mathematical model

KW - Numerical simulation

KW - Polyvinyl alcohol

UR - http://www.scopus.com/inward/record.url?scp=33746898257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746898257&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2005.12.011

DO - 10.1016/j.apm.2005.12.011

M3 - Article

AN - SCOPUS:33746898257

VL - 30

SP - 1497

EP - 1514

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 12

ER -