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| Semi-linear Wave Equations with Effective Damping |
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Citation： |
Marcello D'ABBICCO,Sandra LUCENTE,Michael REISSIG.Semi-linear Wave Equations with Effective Damping[J].Chinese Annals of Mathematics B,2013,34(3):345~380 |
| Page view： 3857
Net amount： 3126 |
Authors： |
Marcello D'ABBICCO; Sandra LUCENTE; Michael REISSIG; |
Foundation： |
a grant of DFG (Deutsche Forschungsgemeinschaft) for the research project “Influence of time-dependent coefficients on semi-linear wave models” (No.RE 961/17-1). |
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| Abstract： |
The authors study the Cauchy problem for the semi-linear damped wave equation $$ u_{tt}-\triangle u+b(t)u_t=f(u), u(0,x)=u_0(x), u_t(0,x)=u_1(x) $$ in any space dimension~$n\geq1$. It is assumed that the time-dependent damping term~$b(t)>0$ is {effective}, and in particular $tb(t)\to\infty$ as $t\to \infty$. The global existence of small energy data solutions for~$|f(u)|\approx |u|^p$ in the supercritical case of $p>1+\frac 2 n$ and $p\leq \frac n{n-2}$ for $n\ge 3$ is proved. |
Keywords： |
Semi-linear equations, Damped wave equations, Critical exponent,Global existence |
Classification： |
35L71 |
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