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Nonexistence of a global solution of a mixed problem for a nonlinear system of equations with integral perturbation in a domain unbounded with respect to time variable

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Nonlinear Oscillations

We study a mixed problem for a nonlinear connected evolution system of equations with integral perturbation in a domain unbounded with respect to the time variable. We prove that a global generalized solution of this problem does not exist.

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References

  1. R. F. Apolaya, H. R. Clark, and A. J. Feitosa, “On a nonlinear coupled system with internal damping,” Electron. J. Different. Equat., 2000, No. 64, 1–17 (2000).

    MathSciNet  Google Scholar 

  2. A. Arosio and S. Spagnolo, “Global solutions of the Cauchy problem for a nonlinear hyperbolic equation,” in: H. Brezis and J.-L. Lions (editors), Nonlinear Partial Differential Equations and Their Applications, Vol. 6, Pitman, Boston (1984), pp. 1–26.

    Google Scholar 

  3. E. Bisignin, “Perturbation of Kirchhoff–Carrier’s operator by Lipschitz functions,” in: Proc. XXXI Bras. Sem. Analysis, Rio de Janeiro (1992).

  4. M. R. Clark and O. A. Lima, “On a mixed problem for a coupled nonlinear system,” Electron. J. Different. Equat., 1997, No. 06, 1–11 (1997).

    MathSciNet  Google Scholar 

  5. M. R. Clark and O. A. Lima, “Existence of solutions for a variational unilateral system,” Electron. J. Different. Equat., 2002, No. 22, 1–18 (2002).

    MathSciNet  Google Scholar 

  6. P. D’Ancona and S. Spagnolo, Nonlinear Perturbation of the Kirchhoff–Carrier Equations, University of Pisa (1992).

  7. M. Hosoya and Y. Yamada, “On some nonlinear wave equations. I. Local existence and regularity of solutions,” J. Fac. Sci. Univ. Tokyo, Sec. IA, Math., 38, 225–238 (1991).

    MathSciNet  MATH  Google Scholar 

  8. J.-L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris (1969).

    MATH  Google Scholar 

  9. M. P. Matos, “Mathematical analysis of the nonlinear model for the vibrations of a string,” Nonlin. Anal., Theory, Meth. Appl., 17, No. 12, 1125–1137 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. A. Medeiros and M. Milla Miranda, “Local solutions for a nonlinear degenerate hyperbolic equation,” Nonlin. Anal., 10, 27–40 (1986).

    Article  MATH  Google Scholar 

  11. L. A. Medeiros, “On some nonlinear perturbation of Kirchhoff–Carrier’s operator,” Comp. Appl. Math., 13, No. 3, 225–233 (1994).

    MathSciNet  MATH  Google Scholar 

  12. S. A. Messaoudi, “A blowup result in a multidimensional semilinear thermoelastic system,” Electron. J. Different. Equat., 2001, No. 30, 1–9 (2001).

    Google Scholar 

  13. M. O. Nechepurenko, “The mixed problem for a nonlinear coupled evolution system in a bounded domain,” Visn. L’viv. Univ., Ser. Mekh.-Mat., 67, 207–223 (2007).

    MATH  Google Scholar 

  14. M. O. Nechepurenko, “Mixed problem for a nonlinear coupled system in unbounded domains,” Mat. Stud., 32, No. 1, 33–44 (2009).

    MathSciNet  MATH  Google Scholar 

  15. M. O. Nechepurenko and G. P. Torgan, “On the existence of a generalized solution of a nonlinear evolution system in a domain unbounded with respect to the time variable,” Ukr. Mat. Visn., 7, No. 1, 49–72 (2010).

    Google Scholar 

  16. S. I. Pokhozhaev, “On one class of quasilinear hyperbolic equations,” Mat. Sb., 96(138), No. 1, 152–166 (1975).

    Google Scholar 

  17. H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen [Russian translation], Mir, Moscow (1978).

    Google Scholar 

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Correspondence to H. R. Bazylyak.

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Translated from Neliniini Kolyvannya, Vol. 14, No. 4, pp. 435–444, October–December, 2011.

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Bazylyak, H.R., Nechepurenko, M.O. Nonexistence of a global solution of a mixed problem for a nonlinear system of equations with integral perturbation in a domain unbounded with respect to time variable. Nonlinear Oscill 14, 461–471 (2012). https://doi.org/10.1007/s11072-012-0170-8

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  • DOI: https://doi.org/10.1007/s11072-012-0170-8

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