About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 801314, 10 pages
http://dx.doi.org/10.1155/2013/801314
Research Article

On Initial-Boundary Value Problems for Hyperbolic Equations in Domains with Conical Points

Department of Mathematics, Hanoi National University of Education, No. 136 Xuan Thuy Street, Hanoi, Vietnam

Received 24 December 2012; Accepted 14 July 2013

Academic Editor: Ağacik Zafer

Copyright © 2013 Nguyen Manh Hung and Nguyen Thanh Anh. 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. M. Dauge, Elliptic Boundary Value Problems on Corner Domains, vol. 1341 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1988. View at Zentralblatt MATH · View at MathSciNet
  2. V. A. Kondrat'ev, “Boundary value problems for elliptic equations in domains with conical or angular points,” Trudy Moskovskogo Matematičeskogo Obščestva, vol. 16, pp. 209–292, 1967, English translation: Transactions of the Moscow Mathematical Society, vol. 16, 1967. View at MathSciNet
  3. V. A. Kozlov, V. G. Maz'ya, and J. Rossmann, Elliptic Boundary Value Problems in Domains with Point Singularities, vol. 52 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1997. View at MathSciNet
  4. A. Y. Kokotov and B. A. Plamenevskiĭ, “On the cauchy-Dirichlet problem for a hyperbolic system in a wedge,” Algebra i Analiz, vol. 11, no. 3, pp. 140–195, 1999. View at MathSciNet
  5. A. Y. Kokotov and B. A. Plamenevskiĭ, “On the asymptotics of solutions to the Neumann problem for hyperbolic systems in domains with conical points,” Algebra i Analiz, vol. 16, no. 3, pp. 56–98, 2004, English translation: Petersburg Mathematical Journal, Vol. 16, no. 3, pp. 477–506, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. N. M. Hung, “Asymptotic behaviour of solutions of the first boundary-value problem for strongly hyperbolic systems near a conical point at the boundary of the domain,” Matematicheskiĭ Sbornik, vol. 190, no. 7, pp. 103–126, 1999, English translation: Sbornik: Mathematics, vol. 190, no. 7, pp. 1035–1058, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  7. N. M. Hung, N. T. Anh, and P. K. Chuc, “On the regularity of the solution for the second initial boundary value problem for hyperbolic systems in domains with conical points,” Boundary Value Problems, vol. 2011, article 17, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. N. M. Hung and B. T. Kim, “On the solvability of the first mixed problem for strongly hyperbolic system in infinite nonsmooth cylinders,” Taiwanese Journal of Mathematics, vol. 12, no. 9, pp. 2601–2618, 2008. View at Zentralblatt MATH · View at MathSciNet
  9. N. M. Hung and J. C. Yao, “Cauchy-Dirichlet problem for second-order hyperbolic equations in cylinders with non-smooth base,” Nonlinear Analysis: Theory Methods & Applications, vol. 70, no. 2, pp. 741–756, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. S. Agranovich, “Elliptic boundary problems,” in Partial Differential Equations, M. S. Agranovich, Yu. V. Egorov, and M. A. Shubin, Eds., vol. 79 of Encyclopaedia of Mathematical Sciences, pp. 1–144, Springer, Berlin, Germany, 1997. View at Zentralblatt MATH · View at MathSciNet
  11. J. Rossmann, “The asymptotics of the solutions of elliptic variational problems in domains with edges on the boundary,” Zeitschrift für Analysis und ihre Anwendungen, vol. 9, no. 3, pp. 565–575, 1990. View at Zentralblatt MATH · View at MathSciNet
  12. N. M. Hung and N. T. Anh, “Regularity of solutions of initial-boundary value problems for parabolic equations in domains with conical points,” Journal of Differential Equations, vol. 245, no. 7, pp. 1801–1818, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. N. M. Hung and N. T. Anh, “The initial-boundary value problems for parabolic equations in domains with conical points,” in Advances in Mathematics Research, A. R. Baswell, Ed., vol. 10, chapter 4, pp. 205–247, Nova Science Publishers, NewYork, NY, USA, 2009.
  14. J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977. View at MathSciNet
  15. R. A. Adams, Sobolev Spaces, Academic Press, 1975. View at Zentralblatt MATH · View at MathSciNet
  16. L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1998. View at MathSciNet
  17. N. M. Hung and N. T. Anh, “Asymptotic formulas for solutions of parameter-depending elliptic boundary-value problems in domains with conical points,” Electronic Journal of Differential Equations, vol. 2009, no. 125, pp. 1–21, 2009. View at Zentralblatt MATH · View at MathSciNet