论文标题
通过依赖空间的阻尼，吸收非线性和多项式衰减数据的溶液对波方程的衰减特性
Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data
论文作者
论文摘要
我们研究了在整个空间或外部结构域中的空间依赖性阻尼和吸收非线性的半线性波方程解决方案的较大时间行为。我们的结果表明了阻尼系数的振幅，非线性的功率以及空间无穷大的初始数据的衰减速率如何确定能量的衰减速率和溶液的$ l^2 $ norm。在附录中，我们还对解决方案的局部和全局存在以及能量方法中使用的权重功能的特性进行了调查。
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the power of the nonlinearity, and the decay rate of the initial data at the spatial infinity determine the decay rates of the energy and the $L^2$-norm of the solution. In Appendix, we also give a survey of basic results on the local and global existence of solutions and the properties of weight functions used in the energy method.
