Large time behavior of solutions for a system of nonlinear damped wave equations
Large time behavior of solutions for a system of nonlinear damped wave equations
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DOI：
10.1016/j.jde.2011.07.034
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发表时间：
2011-12
影响因子：
2.4
通讯作者：
T. Ogawa;H. Takeda
中科院分区：
文献类型：
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作者：
T. Ogawa;H. Takeda
本文考虑半线性阻尼波方程组的Cauchy问题：其中u（t，x）=（u1（t，x），.，um（t，x）），m <$2，j= 1，.，m.我们证明了非线性指数在尖锐条件下解的渐近性态，这是Nishihara（2003）[21]，Hayashi et al.（2004）[9]，Hosono and Ogawa（2004）[10]关于单非线性阻尼波方程结果的自然推广.证明是基于线性阻尼波方程的基本解的Lp-Lq型分解为耗散部分和双曲部分Hosono and Ogawa（2004）[10]，Nishihara（2003）[21]。
We consider the Cauchy problem of the semilinear damped wave system: where u(t,x)=(u1(t,x),…,um(t,x)) with m⩾2 and j=1,…,m. We show the asymptotic behavior of solutions under the sharp condition on the nonlinear exponents, which is a natural extension of the results for the single nonlinear damped wave equations Nishihara (2003) [21], Hayashi et al. (2004) [9], Hosono and Ogawa (2004) [10]. The proof is based on the Lp–Lqtype decomposition of the fundamental solutions of the linear damped wave equations into the dissipative part and hyperbolic part Hosono and Ogawa (2004) [10], Nishihara (2003) [21].