Blow up for the wave equation with a fractional damping

Journal of Applied Analysis

Volumn 11, Issue 1, 2005, Pages 133-144

  Alaimia, M R ^a   Tatar, N E ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Blow up; Caputo's fractional derivative; Integro differential problem; Modified energy functional; Singular kernel

Indexed keywords

EID: 34248208464     PISSN: 14256908     EISSN: 18696082     Source Type: Journal    
DOI: 10.1515/JAA.2005.133     Document Type: Article

References (9)

1. Georgiev, V., Todorova, G., Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differential Equations 109(1994), 295-308.
2. Kirane, M., Tatar, N.-E., Exponential growth for a fractionally damped wave equation, Z. Anal. Anwendungen 22(1) (2003), 167-177. (Pubitemid 36338746)
3. th International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena (Golden, Colorado, June 1998), 638-640, INRIA-SIAM.
4. Messaoudi, S., A blow up result in a multidimensional semilinear thermoelastic system, Electron. J. Differential Equations 2001(30) (2001), 9 pp., (electronic).
5. Oldham, K. B., Spanier, J., The Fractional Calculus, Academic Press, New York-London, 1974.
6. Podlubny, I., Fractional Differential Equations, Math. Sci. Engrg. 198, Academic Press, San Diego, CA, 1999.
7. Samko, S. G., Kilbas, A. A., Marichev, O. I., Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993. (Translated from the 1987 Russian original).
8. Tatar, N.-E., A wave equation with fractional damping, Z. Anal. Anwendungen 22(3) (2003), 609-617. (Pubitemid 37469031)
9. Tatar, N.-E., A blow up result for a fractionally damped wave equation, NoDEA Nonlinear Differential Equations Appl., (to appear).