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Cauchy problem for a class of fourth-order semilinear pseudohyperbolic equations with structural damping

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Abstract

A sufficient condition for the existence of global solutions is established, and the rate of decay of solutions to the Cauchy problem for a semilinear pseudohyperbolic equation with structural damping is found. The nonexistence of global solutions is also investigated. An analogue of the critical Fujita exponent is obtained for the considered problem.

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References

  1. A. M. Nakhushev, Equations of Mathematical Biology (Vysshaya Shkola, Moscow, 1995) [in Russian].

    MATH  Google Scholar 

  2. A. A. Potapov, Fractals in Radio Physics and Radar: Topology of Sample (Universitetskaya Kniga, Moscow, 2005) [in Russian].

    Google Scholar 

  3. E. Mitidieri and S. I. Pohozaev, Proc. Steklov Inst. Math. 234, 1–375 (2001).

    MathSciNet  Google Scholar 

  4. M. Abbicco and M. Reissing, Math. Meth. Appl. Sci. 37, 170–1592 (2014).

    Article  Google Scholar 

  5. Xu Runzhang and Liu Yacheng, J. Math. Anal. Appl. 359, 739–751 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  6. Yu-Zhu Wang, Nonlin. Anal. 70, 65–482 (2009).

    Google Scholar 

  7. A. B. Aliev and B. H. Lichaei, Nonlin. Anal. 72 (7/8), 3275–3288 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. B. Aliev and A. A. Kazymov, Differ. Equations 45 (2), 175–185 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Fujita, J. Fac. Sci. Univ. Tokyo Sect. I 13, 109–124 (1966).

    MATH  MathSciNet  Google Scholar 

  10. A. B. Aliev, Dokl. Akad. Nauk SSSR 240 (2), 249–252 (1978).

    MathSciNet  Google Scholar 

  11. E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton Univ. Press, Princeton, N.J., 1971; Mir, Moscow, 1974).

    Google Scholar 

  12. O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Imbedding Theorems (Wiley, New York, 1978; Nauka, Moscow, 1996).

    MATH  Google Scholar 

  13. I. E. Segal, Ann. Sci. Ecole Norm. Super 4 (1), 459–497 (1968).

    Google Scholar 

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Authors and Affiliations

  1. Azerbaijan Technical University, pr. H. Cavid 25, Baku, AZ 1073, Azerbaijan

    A. B. Aliev

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, ul. B. Vagabzade 9, Baku, AZ 1141, Azerbaijan

    A. B. Aliev & A. F. Pashayev

Authors
  1. A. B. Aliev
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  2. A. F. Pashayev
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Correspondence to A. B. Aliev.

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Original Russian Text © A.B. Aliev, A.F. Pashayev, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 1, pp. 7–10.

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Aliev, A.B., Pashayev, A.F. Cauchy problem for a class of fourth-order semilinear pseudohyperbolic equations with structural damping. Dokl. Math. 92, 651–654 (2015). https://doi.org/10.1134/S1064562415060010

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  • DOI: https://doi.org/10.1134/S1064562415060010

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