Geodesic
Analysis of semilinear elliptic boundary value problem and its applications
Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 2, pp. 259-267.

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A stationary model of the reaction-diffusion type in a three-dimensional domain is considered. Sufficient conditions for the existence and uniqueness of a weak solution to the posed boundary value problem are found. As an example, diffusion models of complex heat exchange and oxygen transfer in biological tissues are considered. 
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A. A. Pishchikov; A. Yu. Chebotarev. Analysis of semilinear elliptic boundary value problem and its applications. Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 2, pp. 259-267. http://geodesic.mathdoc.fr/item/DVMG_2024_24_2_a9/

[1] Modest M. F., Radiative Heat Transfer, Academic Press, 2003

[2] Kovtanyuk A. E., Chebotarev A. Yu., “Statsionarnaya zadacha slozhnogo teploobmena”, Zh. vychisl. matem. i matem. fiz., 54:4 (2014), 191–199

[3] Kovtanyuk A. E., Chebotarev A. Yu., “Nelokalnaya odnoznachnaya razreshimost statsionarnoi zadachi slozhnogo teploobmena”, Zh. vychisl. matem. i matem. fiz., 56:5 (2016), 816–823 | DOI | Zbl

[4] Chebotarev A. Yu., Grenkin G. V., Kovtanyuk A. E., “Inhomogeneous steady-state problem of complex heat transfer”, ESAIM Math. Model. Numer. Anal., 51:6 (2017), 2511-2519 | DOI | MR | Zbl

[5] Valabregue R., Aubert A., Burger J., Bittoun J., Costalat R., “Relation between cerebral blood flow and metabolism explained by a model of oxygen exchange”, J. Cereb. Blood Flow Metab., 23 (2003), 536–545 | DOI

[6] Kovtanyuk Andrey E., Chebotarev Alexander Yu., Botkin Nikolai D., Turova Varvara L., Sidorenko Irina N., Lampe Renee, “Continuum model of oxygen transport in brain”, J. Math. Anal. Appl., 474 (2019), 1352–1363 | DOI | MR | Zbl