Existence and Uniqueness of a Solution to the Cauchy Problem for the Damped Boussinesq Equation
Existence and Uniqueness of a Solution to the Cauchy Problem for the Damped Boussinesq Equation
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DOI：
10.1002/(sici)1099-1476(19960525)19:8
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发表时间：
1996-05
影响因子：
2.9
通讯作者：
V. Varlamov
中科院分区：
文献类型：
--
作者：
V. Varlamov
本文研究小深度粘性流体中长波传播的阻尼Boussinesq方程的Cauchy问题。对于一维、二维和三维空间情形，证明了解的存在唯一性。我们表明，对于不连续的初始扰动，这个解决方案是无限可微的时间t和空间坐标的有界时间间隔上的t > 0。
We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t > 0 on a bounded time interval.