Reaction–diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor

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 bound...

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Vydané v:Nonlinear analysis (Vilnius, Lithuania) Ročník 22; číslo 2; s. 261 - 272
Hlavní autori: Ivanauskas, Feliksas, Laurinavičius, Valdas, Sapagovas, Mifodijus, Neciporenko, Anatolij
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Vilnius University Press 15.03.2017
Predmet:
bioreactor
immobilized enzyme
mathematical modeling
nonlocal boundary condition
PID controller
reaction–diffusion
mathematical modeling
nonlocal boundary condition
immobilized enzyme
PID controller
reaction–diffusion
bioreactor
ISSN:1392-5113, 2335-8963
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Popis
Shrnutí: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. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).
ISSN:1392-5113
2335-8963
DOI:10.15388/NA.2017.2.8