Skip to main content
SpringerLink
Log in

Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion

  • Published:
Acta Applicandae Mathematicae Aims and scope Submit manuscript

Abstract

This paper concerns with the existence, uniqueness and asymptotic behaviour of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented.

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

References

  1. Ackleh, A.S., Ke, L.: Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations. Proc. Am. Math. Soc. 128, 3483–3492 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bainov, D., Simeonov, P.: Integral Inequalities and Applications. Kluwer Academic, Dordrecht (1992)

    MATH  Google Scholar 

  3. Brezis, H.: Analyse Fonctionelle, Theorie et Applications. Mason, Paris (1983)

    Google Scholar 

  4. Capasso, V., Di Libdo, A.: Global attractivity for reaction-diffusion system. The case of nondiagonal matrices. J. Math. Anal. Appl. 177, 510–529 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chipot, M., Lovat, B.: Some remarks on nonlocal elliptic and parabolic problems. Nonlinear Anal. Theory Methods Appl. 30(7), 4619–4627 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cho, Y.J., Dragomir, S.S., Kim, Y.-H.: On some Gronwall type inequalities involving iterated integrals. Math. Commun. 12, 63–73 (2007)

    MATH  Google Scholar 

  7. Eymard, R., Gallouët, T., Herbin, R., Michel, A.: Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Numer. Math. 92(1), 41–82 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Menezes, S.D.: Remarks on weak solution for a nonlocal parabolic problem. Int. J. Math. Math. Sci. 2006, 1–10 (2006)

    Article  MathSciNet  Google Scholar 

  9. Lions, J.L.: Quelques méhodes de résolution des problemes aux limites non linéaires. Dunod Paris (1969)

  10. Oliveira, L.A.F.: On reaction-diffusion system. Electron. J. Differ. Equ. 1998(24), 1–10 (1998)

    Google Scholar 

  11. Rudin, W.: Functional Analysis. Tata McGraw-Hill, New Delhi (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UFSJ, Praça Frei Orlando 170, Cep 36307-352, São João del-Rei, MG, Brazil

    Carlos Alberto Raposo

  2. CI²MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Mauricio Sepúlveda

  3. Departamento de Matemática, Universidad del Bío-Bío, Collao 1202, Casilla 5-C, Concepción, Chile

    Octavio Vera Villagrán

  4. UFPA, Rua Augusto Corrêa 01, CEP 66075-110, Pará, Brazil

    Ducival Carvallo Pereira & Mauro Lima Santos

Authors
  1. Carlos Alberto Raposo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mauricio Sepúlveda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Octavio Vera Villagrán
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ducival Carvallo Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mauro Lima Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauricio Sepúlveda.

Additional information

Partially supported by CMM, Universidad de Chile, and CI2MA, Universidad de Concepción.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raposo, C.A., Sepúlveda, M., Villagrán, O.V. et al. Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion. Acta Appl Math 102, 37–56 (2008). https://doi.org/10.1007/s10440-008-9207-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-008-9207-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation