Homogenization of scalar wave equations with hysteresis
Homogenization of scalar wave equations with hysteresis
复制标题
具有磁滞的标量波动方程的齐次化
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
P. Krejčí
中科院分区：
文献类型：
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作者：
J. Francu;P. Krejčí
本文讨论了一个标量波动方程，
$
ho u_{tt} =（{cal F}[u_x]）_x + f，，$其中
$cal F$是Prandtl-Ishlinskii算子，
$
f$是函数。这个方程描述弹塑性杆的纵向振动。质量密度
$
ho$与Prandtl-Ishlinskii分布函数
$eta$可以依赖于空间变量x。我们证明了相应的初边值问题解的存在性、唯一性和正则性。然后通过考虑具有空间周期数据的上述类型的方程序列来均匀化系统
$
ho^varep $ and
$eta^vareps $，其中空间周期
$vareps $趋向于0。我们确定齐次极限
$
* **
$eta^*$并证明解的收敛性
$u^表示$到解决方案
$u^*$的均匀化方程。
The paper deals with a scalar wave equation of the form
$
ho u_{tt} = ({cal F}[u_x])_x + f ,,$ where
$cal F$ is a Prandtl–Ishlinskii operator and
$
ho, f$ are given functions. This equation describes longitudinal vibrations of an elastoplastic rod. The mass density
$
ho$ and the Prandtl–Ishlinskii distribution function
$eta$ are allowed to depend on the space variable x. We prove existence, uniqueness and regularity of solution to a corresponding initial-boundary value problem. The system is then homogenized by considering a sequence of equations of the above type with spatially periodic data
$
ho^varepsilon$ and
$eta^varepsilon$, where the spatial period
$varepsilon$ tends to 0. We identify the homogenized limits
$
ho^*$ and
$eta^*$ and prove the convergence of solutions
$u^varepsilon$ to the solution
$u^*$ of the homogenized equation.