Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type
Szomolay, Barbara
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 71-84 / Harvested from Czech Digital Mathematics Library
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In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction $$ \ddot{u}= - \gamma \dot{u} + m(\|\nabla u\|^2) \Delta u - \delta |u|^{\alpha }u + f, $$ which is known as degenerate if $m(\cdot )\ge 0$, and non-degenerate if $m(\cdot )\ge m_0 > 0$. We would like to point out that, to the author's knowledge, exponential decay for this type of equations has been studied just for the special cases of $\alpha $. Our aim is to extend the validity of previous results in [5] to $\alpha \ge 0 $ both to the degenerate and non-degenerate cases of $m$. We extend our results to equations with $ \Delta^2$.

Publié le : 2003-01-01
Classification:  35B40,  35L20,  35L70,  35L80,  45K05,  74H45 
@article{119368,
     author = {Barbara Szomolay},
     title = {Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {71-84},
     zbl = {1098.35033},
     mrnumber = {2045846},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119368}
}

Szomolay, Barbara. Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 71-84. http://gdmltest.u-ga.fr/item/119368/

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