Input-output systems in Biology and Chemistry and a class of mathematical models describing them

Erich Bohl; Ivo Marek

Applications of Mathematics (2005)

  • Volume: 50, Issue: 3, page 219-245
  • ISSN: 0862-7940

Abstract

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Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators forming the underlying dynamical systems are (nonlinear) negative M -operators.

How to cite

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Bohl, Erich, and Marek, Ivo. "Input-output systems in Biology and Chemistry and a class of mathematical models describing them." Applications of Mathematics 50.3 (2005): 219-245. <http://eudml.org/doc/33219>.

@article{Bohl2005,
abstract = {Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators forming the underlying dynamical systems are (nonlinear) negative $M$-operators.},
author = {Bohl, Erich, Marek, Ivo},
journal = {Applications of Mathematics},
keywords = {dynamical system; input-output system; chemical network; boundary layer; dynamical system; input-output system; chemical network; boundary layer},
language = {eng},
number = {3},
pages = {219-245},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Input-output systems in Biology and Chemistry and a class of mathematical models describing them},
url = {http://eudml.org/doc/33219},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Bohl, Erich
AU - Marek, Ivo
TI - Input-output systems in Biology and Chemistry and a class of mathematical models describing them
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 219
EP - 245
AB - Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators forming the underlying dynamical systems are (nonlinear) negative $M$-operators.
LA - eng
KW - dynamical system; input-output system; chemical network; boundary layer; dynamical system; input-output system; chemical network; boundary layer
UR - http://eudml.org/doc/33219
ER -

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