Szomolay, Barbara. "Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 71-84. <http://eudml.org/doc/249197>.
@article{Szomolay2003,
abstract = {In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction \[ \ddot\{u\}= - \gamma \dot\{u\} + m(\Vert \nabla u\Vert ^2) \Delta u - \delta |u|^\{\alpha \}u + f, \]
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$.},
author = {Szomolay, Barbara},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymptotic behavior of solutions; hyperbolic PDE of degenerate type; asymptotic behavior of solution; hyperbolic partial differential equation of degenerate type; exponential decay},
language = {eng},
number = {1},
pages = {71-84},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type},
url = {http://eudml.org/doc/249197},
volume = {44},
year = {2003},
}
TY - JOUR
AU - Szomolay, Barbara
TI - Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 71
EP - 84
AB - In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction \[ \ddot{u}= - \gamma \dot{u} + m(\Vert \nabla u\Vert ^2) \Delta u - \delta |u|^{\alpha }u + f, \]
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$.
LA - eng
KW - asymptotic behavior of solutions; hyperbolic PDE of degenerate type; asymptotic behavior of solution; hyperbolic partial differential equation of degenerate type; exponential decay
UR - http://eudml.org/doc/249197
ER -
