Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 407940, 19 pages
Research Article

On Strong Solutions of Regularized Model of a Viscoelastic Medium with Variable Boundary

Department of Mathematics, Voronezh State University, Universitetskaya pl., 1, Voronezh 394 000, Russia

Received 29 September 2011; Accepted 19 October 2011

Academic Editor: Y. Xu

Copyright © 2012 Vladimir Orlov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. P. Orlov and P. E. Sobolewskii, “Investigation of mathematical models of viscoelasticity,” Doklady Akademii Nauk Ukrainskoj SSR Serija A, vol. 10, pp. 31–35, 1989. View at Google Scholar
  2. V. P. Orlov and P. E. Sobolevskiĭ, “On mathematical models of a viscoelasticity with a memory,” Differential and Integral Equations, vol. 4, no. 1, pp. 103–115, 1991. View at Google Scholar
  3. V. G. Zvyagin and V. T. Dmitrienko, “On strong solutions of an initial-boundary value problem for a regularized model of an incompressible viscoelastic medium,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ, no. 9, pp. 24–40, 2004. View at Google Scholar
  4. O. A. Ladyženskaja, “An initial-boundary value problem for the Navier-Stokes equations in domains with boundary changing in time,” Zapiski Naučnyh Seminarov LOMI, vol. 11, pp. 97–128, 1968. View at Google Scholar
  5. V. P. Orlov and V. G. Zvyagin, “On weak solutions of the equations of motion of a viscoelastic medium with variable boundary,” Boundary Value Problems, vol. 2005, no. 3, pp. 215–245, 2005. View at Google Scholar
  6. R. Temam, The Navier-Stokes Equations. Theory and Numerical Analysis, Mir, Moskow, Russia, 1987.
  7. M. S. Birman, N. Y. Vilenkin et al., Functional Analysis, S. G. Krein, Ed., Nauka, Moscow, Russia, 1972.
  8. O. A. Ladyzhenskaya, Mathematical Problems of Viscous Incompressible Fluid, Nauka, Moscow, Russia, 1970.
  9. V. P. Orlov, “On strong solutions of a regularized model of a nonlinearly viscoelastic medium,” Matematicheskie Zametki, vol. 84, no. 2, pp. 238–253, 2008. View at Publisher · View at Google Scholar
  10. V. P. Orlov, Investigation of certain nonlinear parabolic and hyperbolic-parabolic systems of differential equations with a memory, Doctor of Science thesis, Institute of Mathematics of National Academy of Science of Ukraine, Kiev, Ukraine, 1996.
  11. H. Triebel, Theory of Interpolation. Function Spaces. Differential operators, Mir, Moscow, Russia, 1980.
  12. V. V. Pukhnachev, The Motion of a Viscous Fluid with Free Boundary, Novosibirsk. Gos. Univ., Novosibirsk, Russia, 1989.
  13. O. V. Besov, V. P. Ilyin, and N. S. Nicholskii, Integral Prdstavleniya Functions and Embedding Theorems, Nauka, Moscow, Russia, 1975.
  14. P. E. Sobolewskii, “Coercitive inequalities for abstract parabolic equations,” Doklady Akademii Nauk USSR, vol. 157, pp. 52–54, 1964. View at Google Scholar