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Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 447–456 (Mi semr601)  

This article is cited in 6 scientific papers (total in 6 papers)

Differentical equations, dynamical systems and optimal control

Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation

R. V. Brizitskiiab, Zh. Yu. Saritskayaa

a Far Earstern Federal University, str. Sukhanova, 8, 690000, Vladivostok, Russia
b Institute of Applied Mathematics FEB RAS, str. Radio, 7, 690041, Vladivostok, Russia

Abstract: We study the boundary value and optimal control problems for stationary nonlinear convection-diffusion-reaction equation, wherein reaction coefficient depends on concentration of substance. The general form of nonlinear reaction coefficient’s dependence on concentration of substance is offered. Solvability of the boundary value and control problems for convection-diffusion-reaction equation is proved. Nonlocal optimality system for the quadratic nonlinearity is obtained, and local uniqueness of extremal problem’s solution for a particular cost functional is proved with the help of optimality system.

Keywords: convection-diffusion-reaction equation, control problem, optimality system, local uniqueness.

DOI: https://doi.org/10.17377/semi.2015.12.038

Full text: PDF file (164 kB)
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UDC: 517.95
MSC: 35A05
Received June 1, 2015, published August 11, 2015

Citation: R. V. Brizitskii, Zh. Yu. Saritskaya, “Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation”, Sib. Èlektron. Mat. Izv., 12 (2015), 447–456

Citation in format AMSBIB
\Bibitem{BriSar15}
\by R.~V.~Brizitskii, Zh.~Yu.~Saritskaya
\paper Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 447--456
\mathnet{http://mi.mathnet.ru/semr601}
\crossref{https://doi.org/10.17377/semi.2015.12.038}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. V. Brizitskii, Zh. Yu. Saritskaya, A. I. Byrganov, “Multiplicative control problems for nonlinear convection–diffusion–reaction equation”, Sib. elektron. matem. izv., 13 (2016), 352–360  mathnet  crossref
    2. Zh. Yu. Saritskaya, R. V. Brizitskii, “Leading coefficient's recovering problem for nonlinear convection-diffusion-reaction equation”: A. Chesnokov, E. Pruuel, V. Shelukhin, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, IOP Publishing Ltd, 2017, UNSP 012082  crossref  isi  scopus
    3. Zh. Yu. Saritskaya, R. V. Brizitskii, “Boundary value and extremum problems for the nonlinear acoustic model”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 1367–1371  crossref  isi  scopus
    4. R. V. Brizitskii, Zh. Yu. Saritskaya, “Inverse coefficient problems for a non-linear convection–diffusion–reaction equation”, Izv. Math., 82:1 (2018), 14–30  mathnet  crossref  crossref  adsnasa  isi  elib
    5. V R. Brizitskii, Zh. Y. Saritskaya, “Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation”, J. Inverse Ill-Posed Probl., 26:6 (2018), 821–833  crossref  mathscinet  zmath  isi  scopus
    6. R. V. Brizitskii, Zh. Yu. Saritskaya, “Boundary control problem for a nonlinear convection-diffusion-reaction equation”, Comput. Math. Math. Phys., 58:12 (2018), 2053–2063  mathnet  crossref  crossref  isi  elib
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