Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 9
Submit an article Journal homepage
92
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

On a global attractor for the strong solutions of the 2-D wave equation with nonlinear damping

A.Kh. Khanmamedov Faculty of Science, Department of Mathematics, Hacettepe University, Beytepe 06532, Ankara, TurkeyCorrespondence[email protected]
Pages 1283-1301 | Received 09 Jan 2009, Accepted 13 Aug 2009, Published online: 03 Nov 2009

References

  • Raugel , G . 1992 . Une equation des ondes avec amortissment non lineaire dans le cas critique en dimensions trois . C. R. Acad. Sci. Paris 314 (Ser. I) , : 177 – 182 .
  • Feireisl , E . 1992 . Attractors for wave equations with nonlinear dissipation and critical exponent . C. R. Acad. Sci. Paris 315 (Ser I) , : 551 – 555 .
  • Lasiecka , I and Ruzmaikina , AR . 2002 . Finite dimensionality and regularity of attractors for 2-D semilinear wave equation with nonlinear dissipation . J. Math. Anal. Appl. , 270 : 16 – 50 .
  • Chueshov , I and Lasiecka , I . 2004 . Attractors for second-order evolution equations with a nonlinear damping . J. Dyn. Diff. Eqns , 16 ( 2 ) : 469 – 512 .
  • Nakao , M . 2006 . Global attractors for nonlinear wave equations with nonlinear dissipative terms . J. Diff. Eq. , 227 : 204 – 229 .
  • Sun , C , Yang , M and Zhong , C . 2006 . Global attractors for the wave equation with nonlinear damping . J. Diff. Eqns , 227 : 427 – 443 .
  • Khanmamedov , AKh . 2006 . Global attractors for wave equations with nonlinear interior damping and critical exponents . J. Diff. Eqns , 230 : 702 – 719 .
  • Chueshov , I and Lasiecka , I . 2007 . “ Long-time dynamics of semilinear wave equation with nonlinear interior-boundary damping and sources of critical exponents ” . In Contemp. Math. Vol. 426 , 153 – 193 .
  • Chueshov , I and Lasiecka , I . 2008 . Long-time Behavior of Second-order Evolution Equations with Nonlinear Damping , Vol. 195 , AMS, Providence : Memoirs of AMS .
  • Feireisl , E and Zuazua , E . 1993 . Global attractors for semilinear wave equations with locally distributed nonlinear damping and critical exponent . Commun. PDE. , 18 : 1538 – 1555 .
  • Chueshov , I , Lasiecka , I and Toundykov , D . 2008 . Long-term dynamics of semilinear wave equations with nonlinear localized interior damping and a source term of critical exponent . Discr. Contin. Dyn. Syst. , 20 : 459 – 509 .
  • Khanmamedov , AKh . 2008 . Long-time behaviour of wave equations with nonlinear interior damping . Discrete Contin. Dyn. Syst. , 21 : 1185 – 1198 .
  • Ghidaglia , J-M and Temam , R . 1987 . Regularity of the solutions of second order evolution equations and their attractors . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 14 : 485 – 511 .
  • Ladyzhenskaya , OA . 1988 . Attractors of nonlinear evolution problems with dissipation . J. Soviet Math. , 40 : 632 – 640 .
  • Lions , JL and Magenes , E . 1972 . Non-homogeneous Boundary Value Problems and Applications , Vol. I , New York : Springer-Verlag .
  • Temam , R . 1988 . Infinite-dimensional Dynamical Systems in Mechanics and Physics , New York : Springer-Verlag .
  • Kesavan , S . 1989 . Topics in Functional Analysis and Applications , New Delhi : Wiley Eastern Ltd .
  • Babin , AV and Vishik , MI . 1992 . Attractors of Evolution Equations , Amsterdam : North-Holland .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.