Geodesic
Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation $$ u_{tt}-\Delta u +|u|^kj'(u_t)=|u|^{p-1}u \quad \hbox{in }\Omega \times (0,T), $$ where p?1 and j' denotes the derivative of a $C^1$ convex and real value function j. We prove that every weak solution is asymptotically stability, for every m such that 0?m?1, p?k+m and the the initial energy is small; the solutions blows up in finite time, whenever p?k+m and the initial data is positive, but appropriately bounded.
Classification : 35B40
Keywords: wave equation, degenerate damping and source terms, asymptotic stability, blow up of solutions 
@article{EJDE_2007__2007__a87,
     author = {Hu, Qingying and Zhang, Hongwei},
     title = {Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a87/}
}
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Hu, Qingying; Zhang, Hongwei. Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a87/