The energy decay problem for wave equations with nonlinear dissipative terms in $\mathbb{R}^n$
Grozdena TodorovaBorislav Yordanov
35L0535L7037L15wave equationnonlinear dissipationdecay rates
We study the asymptotic behavior of energy for wave equations with nonlinear damping $g(u_t) = |u_t|^{m-1}u_t$ in $\mathbb{R}^n$ ($n \geq 3$) as time $t \to \infty$. The main result shows a polynomial decay rate of energy under the condition $1 < m \leq (n+2)/(n+1)$. Previously, only logarithmic decay rates were found.
Indiana University Mathematics Journal
2007
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10.1512/iumj.2007.56.2963
10.1512/iumj.2007.56.2963
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Indiana Univ. Math. J. 56 (2007) 389 - 416
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