Resolution methods for mathematical models based on differential equations with Stieltjes derivatives

Electronic Journal of Qualitative Theory of Differential Equations

Ignacio Márquez Albés¹  Rodrigo López Pouso² 

[1] Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain;University of Santiago de Compostela, Santiago de Compostela, Spain;

关键词: stieltjes differential equations;    dynamic equations;    separation of variables;    biological models;   

DOI  :  10.14232/ejqtde.2019.1.72

来源: DOAJ

【 摘 要 】

Stieltjes differential equations, i.e. differential equations with usual derivatives replaced by derivatives with respect to given functions (derivators), are useful to model processes which exhibit dead times and/or sudden changes. These advantages of Stieltjes equations are exploited in this paper in the analysis of two real life models: first, the frictionless motion of a vehicle equipped with an electric engine and, second, the evolution of populations of cyanobacteria Spirullina plantensis in semicontinuous cultivation processes. Furthermore, this is not only a paper on applications of known results. For the adequate analysis of our mathematical models we first deduce the solution formula for Stieltjes equations with separate variables. Finally, we show that differential equations with Stieltjes derivatives reduce to ODEs when the derivator is continuous, thus obtaining another resolution method for more general cases.

【 授权许可】

Unknown