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Solvability of a nonlinear parabolic problem arising in modeling surface reactions

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Abstract

We investigate the existence, uniqueness, and long-time behavior of classical solutions to a coupled system of seven nonlinear parabolic equations. Four of them are determined in the interior of a region, and the other three are solved on a part of the boundary. In particular, such systems arise in modeling of surface reactions that involve the bulk diffusion of reactants toward and reaction products from the biocatalyst surface and surface diffusion of the intermediate reaction products.

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References

  1. A. Ambrazevičius, Solvability theorem for a model of a unimolecular heterogeneous reaction with adsorbate diffusion, J. Math. Sci., New York, 184(4):383–398, 2012. Translation from Probl. Math. Anal., 65:13–26, 2012.

  2. A. Ambrazevičius and V. Skakauskas, Solvability of a model for monomer–monomer surface reactions, Nonlinear Anal., Real. World Appl., 35:211–228, 2017.

  3. A. Ambrazevičius and V. Skakauskas, Existence and uniqueness of classical solutions to a nonlinear reaction–diffusion model, Acta Appl. Math., 169(3):559–575, 2020.

    Article  MathSciNet  Google Scholar 

  4. A. Ambrazevičius and V. Skakauskas, Solvability of a coupled quasilinear reaction–diffusion system, Appl. Anal., 169:559–575, 2020.

    Google Scholar 

  5. T.Q. Bao, K. Felnerra, and E. Latosa, Well-posedness and exponential equilibration of a volume–surface reaction–diffusion system with nonlinear boundary coupling, 2017, ar**v:1404.2809v2.

  6. D. Bothe, M. Konhe, S. Maier, and J. Saa, Global strong solutions for a class of heterogeneous catalysis models, J. Math. Anal. Appl., 445:677–709, 2017.

    Article  MathSciNet  Google Scholar 

  7. H.J. Bright and Q.H. Gibson, The oxidation of 1-deuterated glucose by glucose oxidase, J. Biol. Chem., 242(5):994–1003, 1967.

    Article  Google Scholar 

  8. A. Constantin, J. Escher, and Z. Yin, Global solutions for quasilinear parabolic systems, J. Differ. Equations, 197(1): 73–84, 2004.

    Article  MathSciNet  Google Scholar 

  9. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Clifs, NJ, 1964.

    Google Scholar 

  10. A. Ladyzhenskaya, V.A. Solonnikov, and N.N. Uralceva, Linear and Quasi-linear Equation of Parabolic Type, Transl. Math. Monogr., Vol. 23, AMS, Providence, RI, 1968.

  11. J. Morgan and V. Sharma, Uniform bounds for solutions to volume–surface reaction diffusion systems, Differ. Integral Equ., 30(5–6):423–442, 2017.

    MathSciNet  Google Scholar 

  12. J. Morgan and V. Sharma, Martin’s problem for volume–surface reaction–diffusion systems, in B.N. Chetverushkin, W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki, J. Periaux, and O. Pironneau (Eds.), Contributions to Partial Differential Equations and Applications, Comput. Methods Appl. Sci., Vol. 47, Springer, Cham, 2019, pp. 359–370.

  13. C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.

    Google Scholar 

  14. C.V. Pao and W.H. Ruan, Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions, J. Math. Anal. Appl., 333(1):472–499, 2007.

    Article  MathSciNet  Google Scholar 

  15. C.V. Pao and W.H. Ruan, Positive solutions of quasilinear parabolic systems with Dirichlet boundary conditions, J. Differ. Equations, 248(5):1175–1211, 2010.

    Article  MathSciNet  Google Scholar 

  16. C.V. Pao and W.H. Ruan, Quasilinear parabolic and elliptic systems with mixed quasimonotone functions, J. Differ. Equations, 255(7):1515–1553, 2013.

    Article  MathSciNet  Google Scholar 

  17. C.V. Pao and W.H. Ruan, Dynamics of degenerate quasilinear reaction diffusion systems with nonnegative initial functions, J. Differ. Equations, 263(11):7709–7752, 2017.

    Article  MathSciNet  Google Scholar 

  18. M. Pierre, T. Suzuki, and H. Umakoshi, Asymptotic behavior in chemical reaction–diffusion systems with boundary equilibria, J. Appl. Anal. Comput., 8(3):836–858, 2018.

    MathSciNet  Google Scholar 

  19. M. Pierre, T. Suzuki, and R. Zou, Asymptotic behavior of solutions to chemical reaction–diffusion systems, J. Math. Anal. Appl., 450(1):152–168, 2017.

    Article  MathSciNet  Google Scholar 

  20. P.E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal., Theory Methods Appl., 7(4): 387–409, 1983.

  21. Z. Tao, R.A. Raffel, A.-K. Souid, and J. Goodisman, Kinetic studies on enzyme-catalyzed reactions: Oxidation of glucose, decomposition of hydrogen peroxide and their combination, Biophys. J., 96:2977–2988, 2009.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, 03225, Vilnius, Lithuania

    Algirdas Ambrazevičius & Vladas Skakauskas

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  1. Algirdas Ambrazevičius
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  2. Vladas Skakauskas
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Correspondence to Vladas Skakauskas.

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Ambrazevičius, A., Skakauskas, V. Solvability of a nonlinear parabolic problem arising in modeling surface reactions. Lith Math J 63, 428–443 (2023). https://doi.org/10.1007/s10986-023-09609-9

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  • DOI: https://doi.org/10.1007/s10986-023-09609-9

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