Advertisement

Doklady Mathematics

, Volume 98, Issue 2, pp 502–505 | Cite as

Well-Posedness and Spectral Analysis of Volterra Integro-Differential Equations with Singular Kernels

  • V. V. Vlasov
  • N. A. Rautian
Mathematics
  • 4 Downloads

Abstract

Integro-differential equations with unbounded operator coefficients in a Hilbert space are considered. Such equations arise in viscoelasticity theory, thermal physics, and homogenization problems in multiphase media. Initial–boundary value problems for the indicated equations are proved to be well posed, and their spectral analysis is performed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. N. Rabotnov, Elements of Hereditary Solid Mechanics (Nauka, Moscow, 1977; Mir, Moscow, 1980).zbMATHGoogle Scholar
  2. 2.
    A. A. Il’yushin and B. E. Pobedrya, Foundations of the Mathematical Theory of Thermoviscoelasticity (Nauka, Moscow, 1970) [in Russian].Google Scholar
  3. 3.
    M. E. Gurtin and A. C. Pipkin, Arch. Ration. Mech. Anal. 31 (2), 113–126 (1968).CrossRefGoogle Scholar
  4. 4.
    A. Eremenko and S. Ivanov, SIAM J. Math. Anal. 43 (5), 2296–2306 (2011).MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. V. Lykov, Problems in Heat and Mass Transfer (Nauka i Tekhnika, Minsk, 1976) [in Russian].Google Scholar
  6. 6.
    V. V. Vlasov, A. A. Gavrikov, S. A. Ivanov, D. Yu. Knyaz’- kov, V. A. Samarin, and A. S. Shamaev, Sovrem. Probl. Mat. Mekh. 5 (1), 134–155 (2009).Google Scholar
  7. 7.
    V. V. Zhikov, Sb. Math. 191 (7), 973–1014 (2000).MathSciNetCrossRefGoogle Scholar
  8. 8.
    V. V. Vlasov and N. A. Rautian, J. Math. Sci. 179 (3), 390–414 (2011).MathSciNetCrossRefGoogle Scholar
  9. 9.
    V. V. Vlasov, N. A. Rautian, and A. S. Shamaev, J. Math. Sci. 190 (1), 34–65 (2013).MathSciNetCrossRefGoogle Scholar
  10. 10.
    V. V. Vlasov and N. A. Rautian, J. Math. Sci. 233 (4), 555–577 (2018).MathSciNetCrossRefGoogle Scholar
  11. 11.
    V. V. Vlasov and N. A. Rautian, Spectral Analysis of Functional Differential Equations (MAKS, Moscow, 2016) [in Russian].zbMATHGoogle Scholar
  12. 12.
    J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications (Dunod, Paris, 1968).zbMATHGoogle Scholar
  13. 13.
    Tables of Integral Transforms (Bateman Manuscript Project), Ed. by A. Erdélyi (McGraw-Hill, New York, 1954).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations