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

Feliksas Ivanauskas | Zendy; V. Laurinavičius | Zendy; Mifodijus Sapagovas | Zendy; Anatolij Nečiporenko | Zendy

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

Author(s) -

Feliksas Ivanauskas,

V. Laurinavičius,

Mifodijus Sapagovas,

Anatolij Nečiporenko

Publication year - 2017

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2017.2.8

Subject(s) - pid controller , control theory (sociology) , reaction–diffusion system , diffusion , bioreactor , boundary (topology) , diffusion equation , subject (documents) , mathematical analysis , boundary value problem , physics , mathematics , mechanics , computer science , control (management) , chemistry , thermodynamics , engineering , temperature control , artificial intelligence , metric (unit) , operations management , organic chemistry , library science

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.

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