Skip to main content
SpringerLink
Log in

Solvability Theorem for a Mathematical Bimolecular Reaction Model

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

We prove the existence and uniqueness of a classical solution to a coupled system of parabolic and ordinary differential equations, the latter being determined on the boundary of the domain. This system describes the model of surface reactions between carbon monoxide and nitrous oxide.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. This assumption is necessary to prove inequality (7).

References

  1. Ambrazevičius, A.: Solvability of a coupled system of parabolic and ordinary differential equations. Cent. Eur. J. Math. 8(3), 537–547 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ambrazevičius, A.: Existence and uniqueness theorem to a unimolecular heterogeneous catalytic reaction model. Nonlinear Anal., Model. Control 15(4), 405–421 (2010)

    MathSciNet  Google Scholar 

  3. Ambrazevičius, A.: Solvability theorem for a model of a unimolecular heterogeneous reaction with adsorbate diffusion. J. Math. Sci. (N.Y.) 184(4), 383–398 (2012). (Translated from Problems in Mathematical Analysis 65, 13–26 (2012))

    Article  MATH  MathSciNet  Google Scholar 

  4. Ambrazevičius, A.: Solvability of a finite system of parabolic and ordinary differential equations. Lith. Math. J. 53(1), 1–16 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ambrazevičius, A.: The reaction–diffusion problem with dynamical boundary condition. Nonlinear Anal., Theory Methods Appl. 95, 568–579 (2014)

    Article  MATH  Google Scholar 

  6. Belton, D.N., Schmieg, S.J.: Kinetics of CO oxidation by N2O over Rh(111). J. Catal. 138(1), 70–78 (1992)

    Article  Google Scholar 

  7. Fadeev, D.K., Vulix, B.Z., Ural’ceva, N.N.:. Selected chapters of analysis and algebra, LGU (1981). (In Russian)

  8. Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice Hall International, Englewood Clifs (1964)

    MATH  Google Scholar 

  9. Jansen, A.P.J., Hermse, C.G.M.: Optimal structure of bimetalic catalysis for the A+B reaction. Phys. Rev. Lett. 83(18), 3673–3676 (1999)

    Article  Google Scholar 

  10. Ladyzhenskaya, O.A., Solonnikov, V.A., Uralceva, N.N.: Linear and Quasi-Linear Equations of Parabolic Type. Am. Math. Soc., Providence (1968). (English transl.)

    MATH  Google Scholar 

  11. McCabe, R.W., Wong, C.: Steady-state kinetics of the CO–N2O reaction over an alumina-supported rhodium catalyst. J. Catal. 121(2), 422–431 (1990)

    Article  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  15. Skakauskas, V., Katauskis, P.: Numerical solving of coupled systems of parabolic and ordinary differential equations. Nonlinear Anal., Model. Control 15(3), 351–360 (2010)

    MATH  MathSciNet  Google Scholar 

  16. Skakauskas, V., Katauskis, P.: On the kinetics of the Langmuir-type heterogeneous reactions. Nonlinear Anal., Model. Control 16(4), 467–475 (2011)

    MATH  MathSciNet  Google Scholar 

  17. Skakauskas, V., Katauskis, P.: Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces. J. Math. Chem. 50(1), 141–154 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. Skakauskas, V., Katauskis, P., Skvortsov, A.: A reaction–diffusion model of the receptor–toxin–antibody interaction. Theor. Biol. Med. Model. 8, 32 (2011)

    Article  Google Scholar 

  19. Zhdanov, V.P., Kasemo, B.: Kinetic phase transitions in simple reactions on solid surfaces. Surf. Sci. Rep. 20, 111–189 (1994)

    Article  Google Scholar 

  20. Zhdanov, V.P., Kasemo, B.: Mechanism and kinetics of the NO–CO reaction on Rh. Surf. Sci. Rep. 29, 31–90 (1997)

    Article  Google Scholar 

Download references

Acknowledgements

The author thanks V. Skakauskas for the formulation of problem (1)–(5) and fruitful discussions. This work was supported by the Lithuanian Council of Science (Grant No. MIP-052/2012).

Author information

Authors and Affiliations

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

    Algirdas Ambrazevičius

Authors
  1. Algirdas Ambrazevičius
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Algirdas Ambrazevičius.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ambrazevičius, A. Solvability Theorem for a Mathematical Bimolecular Reaction Model. Acta Appl Math 140, 95–109 (2015). https://doi.org/10.1007/s10440-014-9980-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-014-9980-2

Keywords

Search

Navigation