DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR DISSIPATIVE TIMOSHENKO SYSTEM
DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR DISSIPATIVE TIMOSHENKO SYSTEM
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DOI：
10.1142/s0218202508002930
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发表时间：
2008-07
影响因子：
3.5
通讯作者：
Kentaro Ide;S. Kawashima
中科院分区：
文献类型：
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作者：
Kentaro Ide;S. Kawashima
本文考虑一类非线性耗散的Kazhenko系统的初值问题。该系统验证了正则性丢失类型的衰减特性。为了克服这个困难所造成的正则性损失的性质，我们采用时间加权的L2能量方法，结合最佳的L2衰减估计的低阶导数的解决方案。然后在初值条件下证明了解的整体存在性和渐近衰减性。此外，我们还表明，随着时间趋于无穷大，该解逼近用热核叠加表示的线性扩散波。
We consider the initial value problem for a nonlinear version of the dissipative Timoshenko system. This syetem verifies the decay property of regularity-loss type. To overcome this difficulty caused by the regularity-loss property, we employ the time weighed L2 energy method which is combined with the optimal L2 decay estimates for lower order derivatives of solutions. Then we show the global existence and asymptotic decay of solutions under smallness and enough regularity conditions on the initial data. Moreover, we show that the solution approaches the linear diffusion wave expressed in terms of the superposition of the heat kernels as time tends to infinity.