Problems Related to Partial Differential Equations

Abstract

In Chapter 1 on modelling, we saw a general model leading to a partial differential system of equations. These equations describe gas exchanges in a human organism. Similar models are obtained when considering phenomena based on space and time. For instance, another example leading to partial differential equations comes from enzyme biochemistry, where an enzyme E added to a substrate S [48] gives a product in accordance with:

$$ E + S\underset{{{k_{{ - 1}}}}}{\overset{{{k_1}}}{\rightleftharpoons}} ES $$

((9.1))

Then the complex ES is decomposed, giving a product P and the enzyme:

$$ ES\xrightarrow{{{k_2}}}E + P $$

((9.2))

The last reaction is irreversible.