Lower Bounds for the Lifespan of Solutions to Nonlinear Wave Equations in Elasticity
Lower Bounds for the Lifespan of Solutions to Nonlinear Wave Equations in Elasticity
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DOI：
10.1007/978-3-0348-0454-7_10
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
H. Kubo
中科院分区：
文献类型：
--
作者：
H. Kubo
本文研究弹性力学中非线性波动方程在小初值条件下解的寿命。我们论证的主要步骤是构造一个好的近似解。近似的自然选择似乎是自由弹性波方程解的主导项。然而，它并不满足非线性弹性波动方程在适当的意义。为此，我们通过添加高阶项来修改近似。然后，我们能够得到的寿命表示在初始数据和非线性系数的下限。
In this paper we study the lifespan of solutions to nonlinear wave equations in elasticity with small initial data. Main step of our argument is to construct a good approximate solution. A natural choice of the approximation seems to be the leading term of solutions to the free elastic wave equation. However, it does not satisfy the nonlinear elastic wave equation in a suitable sense. For this reason, we modify the approximation by adding a higher-order term. Then, we are able to obtain a lower bound of the lifespan which is expressed in terms of initial data and a coefficient in the nonlinearity.