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On a Stochastic Coupled System of Reaction-Diffusion of Nonlocal Type

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 75))

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Abstract

In this article we investigate the existence and uniqueness of weak solutions for a stochastic nonlinear parabolic coupled system of reaction-diffusion of nonlocal type, and with multiplicative white noise. An important result on the asymptotic behavior of the weak solutions is presented as well.

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References

  1. Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley, New York (1974)

    MATH  Google Scholar 

  2. Breckner, H. (Lisei): Galerkin approximation and the strong solution of the stochastic NavierStokes equation. J. Appl. Math. Stoch. Anal. 13(3), 239–259 (2000)

    Google Scholar 

  3. 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  Google Scholar 

  4. Chipot, M.: The diffusion of a population partly driven by its preferences. Arch. Ration. Mech. Anal. 155, 237–259 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chipot, M., Corrêa, F.J.S.A.: Boundary layer solutions to functional elliptic equations. Bull. Braz. Math. Soc. New Ser. 40(3), 381–393 (2009)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Chipot, M., Lovat, B.: On the asymptotic behaviour of some nonlocal problems. Positivity 3, 65–81 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chipot, M., Rodrigues, J.F.: On a class of nonlocal nonlinear problems. Math. Model. Numer. Anal. 26(3), 447–468 (1992)

    MATH  MathSciNet  Google Scholar 

  9. Coayla-Teran, E.A., Ferreira, J., Magalhães, P.M.D.: Weak solutions for random nonlinear parabolic equations of nonlocal type. Random Oper. Stoch. Equ. 16, 213–222 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Corrêa, F.J.S.A., Menezes, S.D.B., Ferreira, J.: On a class of problems involving a nonlocal operator. Appl. Math. Comput. 147, 475–489 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications, vol. 44. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  12. Gihman, I.I., Skorohod, A.V.: Stochastic Differential Equations. Springer, Berlin (1974)

    Google Scholar 

  13. Jüngel, A.: Diffusive and nondiffusive population models. In: Mathematical Modeling of Collective Behavior in Socio-economic and Life Sciences. Modeling and Simulation in Science, Engineering and Technology, pp. 397–425. Birkhäuser, Boston (2010)

    Google Scholar 

  14. Lepoutre, T., Pierre, M., Rolland, G.: Global well-posedness of a conservative relaxed cross diffusion system. SIAM J. Math. Anal. 44(3), 1674–1693 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  16. Rozovskii, B.L.: Stochastic Evolution Systems. Kluwer, Dordrecht (1990)

    Book  MATH  Google Scholar 

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Acknowledgements

We thank to the referees for useful comments and suggestions.

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Correspondence to E. A. Coayla-Teran .

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Coayla-Teran, E.A., Ferreira, J., de Magalhães, P.M.D., de Oliveira, H.B. (2014). On a Stochastic Coupled System of Reaction-Diffusion of Nonlocal Type. In: Bernardin, C., Gonçalves, P. (eds) From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54271-8_15

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