Nonexistence of solutions to a hyperbolic equation with a time fractional damping

Zeitschrift für Analysis und ihre Anwendungen

Volumn 25, Issue 2, 2006, Pages 131-142

  Kirane, Mokhtar ^a   Tatar, Nasser Eddine ^b  

^a UNIVERSITÉ DE LA ROCHELLE   (France)

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

Author keywords

Fractional damping; Non existence; Nonlinear hyperbolic equations

Indexed keywords

EID: 33744736572     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1281     Document Type: Article

References (20)

1. Baras, P. and Kersner, R., Local and global solvability of a class of semilinear parabolic equations. J. Diff. Eqs. 68 (1987)(2), 238 - 252.
2. Baras, P. and Pierre, M., Problèmes paraboliques semi-linéaires avec donneés mesures. Applicable Anal. 18 (1984), 11 - 149.
3. Baras, P. and Pierre, M., Critère d'existence de solutions positives pour des équations semi-linéaires non monotones. Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), 185 - 212.
4. Georgiev, V. and Todorova, G., Existence of a solution of the wave equation with nonlinear damping and source terms. J. Diff. Eqs. 109 (1994), 295 - 308.
5. Guedda, M. and M. Kirane, M., Criticality for evolution equation (in Russian). Differ. Uravn. 37 (2001) (4), 511 - 520, 574 - 575
6. (translation in Diff. Eqs. 37 (2001)(4), 540 - 550).
7. Kirane, M. and Qafsaoui, M., Global nonexistence for the Cauchy problem of some nonlinear Reaction-Diffusion systems. J. Math. Anal. Appl. 268 (2002)(1), 217 - 243.
8. Kirane, M. and Qafsaoui, M., Fujita's exponent for a semilinear wave equation with linear damping. Adv. Nonlinear Stud. 2 (2002)(1), 41 - 50.
9. Kirane, M. and Tatar, N.-e., Exponential growth for fractionally damped wave equation. Z. Anal. Anwendungen 22 (2003)(1), 167 - 178.
10. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites nonlinéaires. Paris: Dunod; Gauthier-Villars 1969.
11. Mitidieri, E. and Pohozaev, S., A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. Proc. Steklov Inst. Math. 234 (2001), 1 - 383.
12. Nakao, M., Energy decay of the wave equation with a nonlinear dissipative term. Funkcial. Ekvac. 26 (1983), 237 - 250.
13. Podlubny, I., Fractional Differential Equations. Math. Sci. Eng. 198. San Diego: Academic Press 1999.
14. Samko, S. G., Kilbas, A. A. and Marichev, O. I., Fractional Integrals and Derivatives: Theory and Applications. Yverdon: Gordon and Breach 1993 (Engl. trans. from Russian edition 1987).
15. Seredynska, M. and Hanyga, A., Nonlinear Hamiltonian equations with fractional damping. J. Math. Phys. 41 (2000), 2135 - 2156.
16. Tatar, N.-e., A blow-up result for a fractionally damped wave equation. Nonlin. Diff. Eqs. Appl. 12 (2005)(2), 215 - 226.
17. Tatar, N.-e., A wave equation with fractional damping. Z. Anal. Anwendungen 22 (2003)(3), 609 - 617.
18. Todorova, G. and Yordanov, B., Critical exponent for nonlinear wave equations with damping. J. Diff. Eqs. 174 (2001), 464 - 489.
19. Zhang, Q. S., Blow up and global existence of solutions to an inhomogeneous parabolic system. J. Diff. Eqs. 147 (1998)(1), 155 - 183.
20. Zhang, Q. S., Blow up results for nonlinear parabolic equations on manifolds. Duke Math. J. 97 (1999)(3), 515 - 539.