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Existence and Uniqueness Theorem for a Model of Bimolecular Surface Reactions

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Ukrainian Mathematical Journal Aims and scope

We prove the existence and uniqueness of classical solutions to a coupled system of parabolic and ordinary differential equations in which the latter are determined on the boundary. This system describes a model of bimolecular surface reaction between carbon monoxide and nitrous oxide running on supported rhodium in the case of slow desorption of the products.

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References

  1. A. Ambrazevičius, “Solvability of a coupled system of parabolic and ordinary differential equations,” Centr. Eur. J. Math., 8, No. 3, 537–547 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Ambrazevičius, “Existence and uniqueness theorem to a unimolecular heterogeneous catalytic reaction model,” Nonlin. Anal. Model. Control, 15, No. 4, 405–421 (2010).

    MathSciNet  MATH  Google Scholar 

  3. A. Ambrazevičius, “Solvability theorem for a model of a unimolecular heterogeneous reaction with adsorbate diffusion,” J. Math. Sci., 184, No. 4, 383–398 (2012); Transl.: Probl. Math. Anal., 65, 13–26 (2012).

  4. A. Ambrazevičius, “Solvability theorem for a mathematical bimolecular reaction model,” Acta Appl. Math., 140, 95–109 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, NJ (1964).

    MATH  Google Scholar 

  6. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, “Linear and quasilinear equation of parabolic type,” in: Transl. Math. Monogr., Vol. 23, American Mathematical Society, Providence, RI, (1968).

  7. A. P. J. Jansen and C. G. M. Hermse, “Optimal structure of bimetallic catalysis for the A+B reaction,” Phys. Rev. Lett., 83, No. 18, 3673–3676 (1999).

    Article  Google Scholar 

  8. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum, New York (1992).

    MATH  Google Scholar 

  9. V. Skakauskas and P. Katauskis, “Numerical solving of coupled systems of parabolic and ordinary differential equations,” Nonlin. Anal. Model. Control, 15, No. 3, 351–360 (2010).

    MathSciNet  MATH  Google Scholar 

  10. V. Skakauskas and P. Katauskis, “Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces,” J. Math. Chem., 50, No. 1, 141–154 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. Skakauskas and P. Katauskis, “On the kinetics of the Langmuir-type heterogeneous reactions,” Nonlin. Anal. Model. Control, 16, No. 4, 467–475 (2011).

    MathSciNet  MATH  Google Scholar 

  12. V. P. Zhdanov and B. Kasemo, “Kinetic phase transitions in simple reactions on solid surfaces,” Surface Sci. Rep., 20, No. 3, 111–189 (1994).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Vilnius University, Vilnius, Lithuania

    A. Ambrazevičius

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  1. A. Ambrazevičius
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 7, pp. 877–888, July, 2017.

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Ambrazevičius, A. Existence and Uniqueness Theorem for a Model of Bimolecular Surface Reactions. Ukr Math J 69, 1019–1033 (2017). https://doi.org/10.1007/s11253-017-1412-9

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  • DOI: https://doi.org/10.1007/s11253-017-1412-9

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