| Title |
Reaction-diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor / |
| Authors |
Ivanauskas, Feliksas ; Laurinavičius, Valdas Stanislovas ; Sapagovas, Mifodijus ; Nečiporenko, Anatolij |
| DOI |
10.15388/NA.2017.2.8 |
| Full Text |
|
| Is Part of |
Nonlinear analysis : modelling and control.. Vilnius : Vilnius University Institute of Mathematics and Informatics. 2017, Vol. 22, No. 2, p. 261-272.. ISSN 1392-5113 |
| Keywords [eng] |
mathematical modeling ; nonlocal boundary condition ; reaction–diffusion ; immobilized enzyme ; bioreactor ; PID controller |
| Abstract [eng] |
We study a system of two parabolic nonlinear reaction–diffusion equations subject to a nonlocal boundary condition. This system of nonlinear equations is used for mathematical modeling of biosensors and bioreactors. The integral-type nonlocal boundary condition links the solution on the system boundary to the integral of the solution within the system inner range. This integral plays an important role in the nonlocal boundary condition and in the general formulation of the boundary value problem. The solution at boundary points is calculated using the integral combined with the proportional-integral-derivative controller algorithm. The mathematical model was applied for the modeling and control of drug delivery systems when prodrug is converted into active form in the enzyme-containing bioreactor before the delivering into body. The linear, exponential, and stepwise protocols of drug delivery were investigated, and the corresponding mathematical models for the prodrug delivery were created. |
| Published |
Vilnius : Vilnius University Institute of Mathematics and Informatics |
| Type |
Journal article |
| Language |
English |
| Publication date |
2017 |
| CC license |
|
